$$\frac{2x-3}{2} = \frac{3}{x+4}$$
Answer
$$ \begin{matrix}x_1 = 2 & x_2 = -\dfrac{ 9 }{ 2 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{2x-3}{2} &= \frac{3}{x+4}&& \text{multiply ALL terms by } \color{blue}{ 2(x+4) }. \\[1 em]2(x+4)\frac{2x-3}{2} &= 2(x+4)\cdot\frac{3}{x+4}&& \text{cancel out the denominators} \\[1 em]2x^2+5x-12 &= 6&& \text{move all terms to the left hand side } \\[1 em]2x^2+5x-12-6 &= 0&& \text{simplify left side} \\[1 em]2x^2+5x-18 &= 0&& \\[1 em] \end{aligned} $$
$ 2x^{2}+5x-18 = 0 $ is a quadratic equation.
You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this equation.
This page was created using
Polynomial Equations Solver