Question
$$\frac{4}{x} = 40-2x$$
Answer
$$ \begin{matrix}x_1 = 10-7 \sqrt{ 2 } & x_2 = 10+7 \sqrt{ 2 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{4}{x} &= 40-2x&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]x\cdot\frac{4}{x} &= x\cdot40-x\cdot2x&& \text{cancel out the denominators} \\[1 em]4 &= 40x-2x^2&& \text{simplify right side} \\[1 em]4 &= -2x^2+40x&& \text{move all terms to the left hand side } \\[1 em]4+2x^2-40x &= 0&& \text{simplify left side} \\[1 em]2x^2-40x+4 &= 0&& \\[1 em] \end{aligned} $$
$ 2x^{2}-40x+4 = 0 $ is a quadratic equation.
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