$$\frac{x}{5} = \frac{3}{x}-2$$
Answer
$$ \begin{matrix}x_1 = -5-2 \sqrt{ 10 } & x_2 = -5+2 \sqrt{ 10 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{x}{5} &= \frac{3}{x}-2&& \text{multiply ALL terms by } \color{blue}{ 5x }. \\[1 em]5x \cdot \frac{x}{5} &= 5x\cdot\frac{3}{x}-5x\cdot2&& \text{cancel out the denominators} \\[1 em]x^2 &= 15-10x&& \text{move all terms to the left hand side } \\[1 em]x^2-15+10x &= 0&& \text{simplify left side} \\[1 em]x^2+10x-15 &= 0&& \\[1 em] \end{aligned} $$
$ x^{2}+10x-15 = 0 $ is a quadratic equation.
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