$$\frac{4}{x} = \frac{x}{3x-5}$$
Answer
$$ \begin{matrix}x_1 = 2 & x_2 = 10 \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{4}{x} &= \frac{x}{3x-5}&& \text{multiply ALL terms by } \color{blue}{ x(3x-5) }. \\[1 em]x(3x-5)\cdot\frac{4}{x} &= x(3x-5)\frac{x}{3x-5}&& \text{cancel out the denominators} \\[1 em]12x-20 &= x^2&& \text{move all terms to the left hand side } \\[1 em]12x-20-x^2 &= 0&& \text{simplify left side} \\[1 em]-x^2+12x-20 &= 0&& \\[1 em] \end{aligned} $$
$ -x^{2}+12x-20 = 0 $ is a quadratic equation.
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