{"id":309221,"date":"2026-07-28T12:40:22","date_gmt":"2026-07-28T10:40:22","guid":{"rendered":"https:\/\/sherpas.com\/blog\/?p=309221"},"modified":"2026-07-29T12:45:04","modified_gmt":"2026-07-29T10:45:04","slug":"resoudre-equation-maths","status":"publish","type":"post","link":"https:\/\/sherpas.com\/blog\/resoudre-equation-maths\/","title":{"rendered":"Comment r\u00e9soudre une \u00e9quation en maths : Guide pratique et d\u00e9taill\u00e9"},"content":{"rendered":"<section class=\"you-know\"><div class=\"you-know__title\"><p>\ud83e\udde0 \u00c0 retenir :<\/p><\/div><div class=\"you-know__text\"><ul>\n<li>Pour <strong>r\u00e9soudre une \u00e9quation<\/strong>, il faut isoler la variable d\u2019un c\u00f4t\u00e9 du signe \u00e9gal afin de trouver sa valeur.<\/li>\n<li>Chaque type d\u2019\u00e9quation, comme les \u00e9quations lin\u00e9aires ou quadratiques, poss\u00e8de une m\u00e9thode de r\u00e9solution sp\u00e9cifique.<\/li>\n<li>La formule quadratique, la factorisation et l\u2019usage des logarithmes sont des techniques pour solutionner les cas complexes.<\/li>\n<\/ul><\/div><\/section><p>Les \u00e9quations math\u00e9matiques sont omnipr\u00e9sentes dans plusieurs domaines tels que la finance, la physique, et l\u2019ing\u00e9nierie. Comprendre <strong>comment r\u00e9soudre ces \u00e9quations<\/strong> est essentiel pour ma\u00eetriser les concepts fondamentaux des math\u00e9matiques. Cet article fournit une approche structur\u00e9e pour r\u00e9soudre diff\u00e9rents types d\u2019\u00e9quations, en explorant m\u00e9thodiquement chaque \u00e9tape du processus.<\/p>\n\n\n<h2 class=\"wp-block-heading\" id=\"comprendre-les-bases-des-equations\">Comprendre les bases des \u00e9quations<\/h2>\n\n<p>Avant de plonger dans les techniques de r\u00e9solution, il est important de bien comprendre ce qu\u2019est une \u00e9quation. Une <strong>\u00e9quation<\/strong> est une expression math\u00e9matique qui affirme que deux choses sont \u00e9gales. La pr\u00e9sence d\u2019une ou plusieurs <strong>variables<\/strong> (repr\u00e9sent\u00e9es g\u00e9n\u00e9ralement par des lettres comme x, y, z) constitue un \u00e9l\u00e9ment cl\u00e9 de toute \u00e9quation. Le but est de trouver la valeur de cette ou ces inconnues.<\/p>\n\n<h3 class=\"wp-block-heading\" id=\"types-dequations-courantes\">Types d\u2019\u00e9quations courantes<\/h3>\n\n<p>Il existe plusieurs types d\u2019\u00e9quations que vous pouvez rencontrer :<\/p>\n  <ul>\n    <li><p>\u00c9quations lin\u00e9aires<\/p><\/li>\n    <li><p>\u00c9quations quadratiques<\/p><\/li>\n    <li><p>\u00c9quations exponentielles<\/p><\/li>\n    <li><p>\u00c9quations logarithmiques<\/p><\/li>\n  <\/ul>\n<p>Chacune de ces \u00e9quations n\u00e9cessite une m\u00e9thode sp\u00e9cifique pour trouver sa solution avec pr\u00e9cision et rapidit\u00e9.<\/p>\n\n<div style=\"position:relative;overflow:hidden;padding-top:56.25%\"><iframe style=\"position:absolute;top:0;left:0;width:95%;height:100%;border:0\" src=\"https:\/\/www.youtube.com\/embed\/uV_EmbYu9_E?si=qxQ5ePGoWQshUNzq&#038;controls=0\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" allowfullscreen><\/iframe><\/div>\n  \n\n<h2 class=\"wp-block-heading\" id=\"methodes-de-resolution-dequations-lineaires\">M\u00e9thodes de r\u00e9solution d\u2019\u00e9quations lin\u00e9aires<\/h2>\n\n<p>Les <strong>\u00e9quations lin\u00e9aires<\/strong> sont parmi les plus simples \u00e0 r\u00e9soudre. Elles prennent g\u00e9n\u00e9ralement la forme ax + b = c.<\/p>\n\n<h3 class=\"wp-block-heading\" id=\"utiliser-laddition-et-la-soustraction\">Utiliser l\u2019addition et la soustraction<\/h3>\n\n<p>La premi\u00e8re \u00e9tape consiste souvent \u00e0 <strong>isoler la variable<\/strong> sur un c\u00f4t\u00e9 de l\u2019\u00e9quation. Par exemple, dans l\u2019\u00e9quation 2x + 4 = 8, nous pouvons soustraire 4 de chaque c\u00f4t\u00e9 pour obtenir :<\/p>\n  <math><mn>2<\/mn><mi>x<\/mi><mo>+<\/mo><mn>4<\/mn><mo>&#8211;<\/mo><mn>4<\/mn><mo>=<\/mo><mn>8<\/mn><mo>&#8211;<\/mo><mn>4<\/mn><mo \/><mn>2<\/mn><mi>x<\/mi><mo>=<\/mo><mn>4<\/mn><\/math>\n\n<h3 class=\"wp-block-heading\" id=\"appliquer-la-division-et-la-multiplication\">Appliquer la division et la multiplication<\/h3>\n\n<p>Ensuite, il ne reste qu\u2019\u00e0 diviser chaque c\u00f4t\u00e9 par le <strong>coefficient devant la variable<\/strong>. Pour notre \u00e9quation pr\u00e9c\u00e9dente :<\/p>\n  <math><mn>2<\/mn><mi>x<\/mi><mo>=<\/mo><mn>4<\/mn><mo \/><mi>x<\/mi><mo>=<\/mo><mfrac><mn>4<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>2<\/mn><\/math>\n\n<div style=\"justify-content:center;align-items:center;margin-top:5px;margin-bottom:5px\"><img decoding=\"async\" src=\"https:\/\/xapbm7c37i.cloudimg.io\/https:\/\/sherpas.com\/p\/files\/photos\/maths\/resoudre-equation-maths-2.webp?w=640&#038;q=95\" alt=\"Image qui repr\u00e9sente la R\u00e9solution d\u2019une \u00c9quation math\u00e9matique\" width=\"640\" height=\"400\" style=\"width:100%;max-width:500px;height:auto;margin:0.9rem 0 0.9rem 0\" loading=\"lazy\"><\/div>\n  \n\n<h2 class=\"wp-block-heading\" id=\"resolution-des-equations-quadratiques\">R\u00e9solution des \u00e9quations quadratiques<\/h2>\n\n<p>Les <strong>\u00e9quations quadratiques<\/strong> sont de la forme ax\u00b2 + bx + c = 0. Voici diff\u00e9rentes m\u00e9thodes pour les r\u00e9soudre :<\/p>\n\n<h3 class=\"wp-block-heading\" id=\"formule-quadratique\">Formule quadratique<\/h3>\n\n<p>Cette formule est un outil universel pour r\u00e9soudre toutes les \u00e9quations quadratiques. Elle se pr\u00e9sente sous la forme :<\/p>\n<p><math><mi>x<\/mi><mo>=<\/mo><mo>&#8211;<\/mo><mi>b<\/mi><mo>\u00b1<\/mo><msqrt><msup><mi>b<\/mi><mn>2<\/mn><\/msup><mo>&#8211;<\/mo><mn>4<\/mn><mi>a<\/mi><mi>c<\/mi><\/msqrt><mo>\/<\/mo><mn>2<\/mn><mi>a<\/mi><\/math><\/p>\n<p>Par exemple, pour l\u2019\u00e9quation 2x\u00b2 + 3x &#8211; 2 = 0 :<\/p>\n<p><math><mi>a<\/mi><mo>=<\/mo><mn>2<\/mn><mo>,<\/mo><mi>b<\/mi><mo>=<\/mo><mn>3<\/mn><mo>,<\/mo><mi>c<\/mi><mo>=<\/mo><mo>&#8211;<\/mo><mn>2<\/mn><mo \/><mi>Discriminant<\/mi><mo>=<\/mo><msup><mi>b<\/mi><mn>2<\/mn><\/msup><mo>&#8211;<\/mo><mn>4<\/mn><mi>a<\/mi><mi>c<\/mi><mo>=<\/mo><msup><mn>3<\/mn><mn>2<\/mn><\/msup><mo>&#8211;<\/mo><mn>4<\/mn><mo>*<\/mo><mn>2<\/mn><mo>*<\/mo><mo>&#8211;<\/mo><mn>2<\/mn><mo>=<\/mo><mn>9<\/mn><mo>+<\/mo><mn>16<\/mn><mo>=<\/mo><mn>25<\/mn><mo \/><mi>Racine carr\u00e9e du discriminant<\/mi><mo>=<\/mo><msqrt><mn>25<\/mn><\/msqrt><mo>=<\/mo><mn>5<\/mn><\/math><\/p>\n<p>Donc,<\/p>\n<p><math><mi>x<\/mi><mo>=<\/mo><mfrac><mo>(<\/mo><mo>&#8211;<\/mo><mn>3<\/mn><mo>\u00b1<\/mo><mn>5<\/mn><mo>)<\/mo><mn>4<\/mn><\/mfrac><mo \/><mi>x1<\/mi><mo>=<\/mo><mfrac><mo>(<\/mo><mo>&#8211;<\/mo><mn>3<\/mn><mo>+<\/mo><mn>5<\/mn><mo>)<\/mo><mn>4<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>2<\/mn><mn>4<\/mn><\/mfrac><mo>=<\/mo><mn>0.5<\/mn><mo \/><mi>x2<\/mi><mo>=<\/mo><mfrac><mo>(<\/mo><mo>&#8211;<\/mo><mn>3<\/mn><mo>&#8211;<\/mo><mn>5<\/mn><mo>)<\/mo><mn>4<\/mn><\/mfrac><mo>=<\/mo><mo>&#8211;<\/mo><mfrac><mn>8<\/mn><mn>4<\/mn><\/mfrac><mo>=<\/mo><mo>&#8211;<\/mo><mn>2<\/mn><\/math><\/p>\n\n\n<h3 class=\"wp-block-heading\" id=\"factorisation\">Factorisation<\/h3>\n\n\n<div style=\"position:relative;overflow:hidden;padding-top:56.25%\"><iframe style=\"position:absolute;top:0;left:0;width:95%;height:100%;border:0\" src=\"https:\/\/www.youtube.com\/embed\/sr_vOR2ALhw?si=IhgGzlUgds2Y3AeA&#038;controls=0\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" allowfullscreen><\/iframe><\/div>\n\n<p>Si une \u00e9quation peut \u00eatre <strong>factoris\u00e9e facilement<\/strong>, cela simplifie grandement la t\u00e2che. Par exemple :<\/p>\n<p><math><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>&#8211;<\/mo><mn>5<\/mn><mi>x<\/mi><mo>+<\/mo><mn>6<\/mn><mo>=<\/mo><mn>0<\/mn><mo \/><mo>(<\/mo><mi>x<\/mi><mo>&#8211;<\/mo><mn>2<\/mn><mo>)<\/mo><mo>(<\/mo><mi>x<\/mi><mo>&#8211;<\/mo><mn>3<\/mn><mo>)<\/mo><mo>=<\/mo><mn>0<\/mn><mo \/><mi>x<\/mi><mo>&#8211;<\/mo><mn>2<\/mn><mo>=<\/mo><mn>0<\/mn><mo \/>ou<mo \/><mi>x<\/mi><mo>&#8211;<\/mo><mn>3<\/mn><mo>=<\/mo><mn>0<\/mn><mo \/><mi>x<\/mi><mo>=<\/mo><mn>2<\/mn><mo \/>ou<mo \/><mi>x<\/mi><mo>=<\/mo><mn>3<\/mn><\/math><\/p>\n\n\n<h2 class=\"wp-block-heading\" id=\"traiter-les-equations-exponentielles-et-logarithmiques\">Traiter les \u00e9quations exponentielles et logarithmiques<\/h2>\n\n<p>Ces \u00e9quations peuvent \u00eatre plus complexes mais sont aussi r\u00e9solvables via des \u00e9tapes syst\u00e9matiques.<\/p>\n\n<h3 class=\"wp-block-heading\" id=\"equations-exponentielles\">\u00c9quations exponentielles<\/h3>\n\n<p>Consid\u00e9rons une \u00e9quation de la forme a<sup>x<\/sup> = b.<\/p>\n<p>Pour r\u00e9soudre celle-ci, prenez le <strong>logarithme naturel<\/strong> de chaque c\u00f4t\u00e9 :<\/p>\n<p><math><mi>ln<\/mi><mo>(<\/mo><msup><mi>a<\/mi><mi>x<\/mi><\/msup><mo>)<\/mo><mo>=<\/mo><mi>ln<\/mi><mo>(<\/mo><mi>b<\/mi><mo>)<\/mo><mo \/><mi>x<\/mi><mi>ln<\/mi><mo>(<\/mo><mi>a<\/mi><mo>)<\/mo><mo>=<\/mo><mi>ln<\/mi><mo>(<\/mo><mi>b<\/mi><mo>)<\/mo><mo \/><mi>x<\/mi><mo>=<\/mo><mfrac><mi>ln<\/mi><mo>(<\/mo><mi>b<\/mi><mo>)<\/mo><mi>ln<\/mi><mo>(<\/mo><mi>a<\/mi><mo>)<\/mo><\/mfrac><\/math><\/p>\n<p>Exemple : 2<sup>x<\/sup> = 8<\/p>\n<p><math><mi>ln<\/mi><mo>(<\/mo><msup><mn>2<\/mn><mi>x<\/mi><\/msup><mo>)<\/mo><mo>=<\/mo><mi>ln<\/mi><mo>(<\/mo><mn>8<\/mn><mo>)<\/mo><mo \/><mi>x<\/mi><mi>ln<\/mi><mo>(<\/mo><mn>2<\/mn><mo>)<\/mo><mo>=<\/mo><mi>ln<\/mi><mo>(<\/mo><mn>8<\/mn><mo>)<\/mo><mo \/><mi>x<\/mi><mo>=<\/mo><mfrac><mi>ln<\/mi><mo>(<\/mo><mn>8<\/mn><mo>)<\/mo><mi>ln<\/mi><mo>(<\/mo><mn>2<\/mn><mo>)<\/mo><\/mfrac><mo>=<\/mo><mn>3<\/mn><\/math><\/p>\n\n\n<h3 class=\"wp-block-heading\" id=\"equations-logarithmiques\">\u00c9quations logarithmiques<\/h3>\n\n<p>Pour une \u00e9quation de la forme log<sub>a<\/sub>(x) = b :<\/p>\n<p>Transformez-la en sa <strong>forme exponentielle<\/strong> :<\/p>\n<p><math><mi>x<\/mi><mo>=<\/mo><msup><mi>a<\/mi><mi>b<\/mi><\/msup><\/math><\/p>\n<p>Exemple : log<sub>2<\/sub>(x) = 3<\/p>\n<p><math><mi>x<\/mi><mo>=<\/mo><msup><mn>2<\/mn><mn>3<\/mn><\/msup><mo>=<\/mo><mn>8<\/mn><\/math><\/p>\n\n\n<h2 class=\"wp-block-heading\" id=\"utiliser-des-outils-de-calculs\">Utiliser des outils de calculs<\/h2>\n\n<p>De nombreux logiciels et calculateurs en ligne peuvent faciliter la r\u00e9solution d\u2019\u00e9quations complexes.<\/p>\n\n<h3 class=\"wp-block-heading\" id=\"avantages-des-outils-numeriques\">Avantages des outils num\u00e9riques<\/h3>\n\n<p>Les <strong>outils num\u00e9riques<\/strong> permettent de gagner du temps et de r\u00e9duire les erreurs humaines gr\u00e2ce \u00e0 :<\/p>\n  <ul>\n    <li>Calcul pr\u00e9cis et rapide<\/li>\n    <li>Sauvegarde des solutions pour future r\u00e9f\u00e9rence<\/li>\n    <li>Possibilit\u00e9 d\u2019explorer des graphiques associ\u00e9s aux \u00e9quations<\/li>\n  <\/ul>\n\n<h3 class=\"wp-block-heading\" id=\"calculatrices-programmables\">Calculatrices programmables<\/h3>\n\n<p>Les <strong>calculatrices modernes<\/strong> offrent aussi des fonctions de programmation pour r\u00e9soudre rapidement plusieurs types d\u2019\u00e9quations. Par exemple, TI-83 et Casio FX-CG50 sont populaires dans les classes de math\u00e9matiques.<\/p>\n<div style=\"line-height:1.7;margin-top:0.75rem;margin-bottom:0.25rem;letter-spacing:-0.01em\">Nos autres articles sur <a href=\"https:\/\/sherpas.com\/blog\/algebre-fonctions\/\">l\u2019alg\u00e8bre et les fonctions<\/a> :<br><ul>\n<li><a href=\"https:\/\/sherpas.com\/blog\/arithmetique\/\">Arithm\u00e9tique<\/a><\/li>\n<li><a href=\"https:\/\/sherpas.com\/blog\/vecteurs\/\">Vecteurs<\/a><\/li>\n<li><a href=\"https:\/\/sherpas.com\/blog\/algebre-lineaire\/\">Alg\u00e8bre Lin\u00e9aire<\/a><\/li>\n<li><a href=\"https:\/\/sherpas.com\/blog\/fonctions-mathematiques\/\">Fonctions Math\u00e9matiques<\/a><\/li>\n<li><a href=\"https:\/\/sherpas.com\/blog\/suite-arithmetique-geometrique\/\">Suites Arithm\u00e9tiques et G\u00e9om\u00e9triques<\/a><\/li>\n<li><a href=\"https:\/\/sherpas.com\/blog\/fonction-logarithme-decimal\/\">Fonction Logarithmique<\/a><\/li>\n<li><a href=\"https:\/\/sherpas.com\/blog\/fonctions-affines\/\">Fonctions Affines<\/a><\/li>\n<li><a href=\"https:\/\/sherpas.com\/blog\/developper-expression-maths\/\">D\u00e9veloppement Alg\u00e9brique<\/a><\/li>\n<li><a href=\"https:\/\/sherpas.com\/blog\/polynome-second-degre\/\">Polyn\u00f4mes du Second Degr\u00e9<\/a><\/li>\n<li><a href=\"https:\/\/sherpas.com\/blog\/fractions\/\">Fractions<\/a><\/li>\n<li><a href=\"https:\/\/sherpas.com\/blog\/equations-quadratiques\/\">\u00c9quations Quadratiques<\/a><\/li>\n<li><a href=\"https:\/\/sherpas.com\/blog\/definition-la-division-euclidienne\/\">Division Euclidienne<\/a><\/li>\n<\/ul><\/div>\n\n<div class=\"kk-star-ratings kksr-auto kksr-align-center kksr-valign-bottom\"\n    data-payload='{&quot;align&quot;:&quot;center&quot;,&quot;id&quot;:&quot;309221&quot;,&quot;slug&quot;:&quot;default&quot;,&quot;valign&quot;:&quot;bottom&quot;,&quot;ignore&quot;:&quot;&quot;,&quot;reference&quot;:&quot;auto&quot;,&quot;class&quot;:&quot;&quot;,&quot;count&quot;:&quot;0&quot;,&quot;legendonly&quot;:&quot;&quot;,&quot;readonly&quot;:&quot;&quot;,&quot;score&quot;:&quot;0&quot;,&quot;starsonly&quot;:&quot;&quot;,&quot;best&quot;:&quot;5&quot;,&quot;gap&quot;:&quot;5&quot;,&quot;greet&quot;:&quot;Tu as aim\u00e9 cet article ?&quot;,&quot;legend&quot;:&quot;0\\\/5 - (0 vote)&quot;,&quot;size&quot;:&quot;24&quot;,&quot;title&quot;:&quot;Comment r\u00e9soudre une \u00e9quation en maths : Guide pratique et d\u00e9taill\u00e9&quot;,&quot;width&quot;:&quot;0&quot;,&quot;_legend&quot;:&quot;{score}\\\/{best} - ({count} {votes})&quot;,&quot;font_factor&quot;:&quot;1.25&quot;}'>\n            \n<div class=\"kksr-stars\">\n    \n<div class=\"kksr-stars-inactive\">\n            <div class=\"kksr-star\" data-star=\"1\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; 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