Question
$$\frac{4}{x} = \frac{15}{4x}$$
Answer
$$ \begin{matrix}x_1 = -4 \dfrac{\sqrt{ 15 }}{ 15 } & x_2 = \dfrac{ 4 \sqrt{ 15}}{ 15 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{4}{x} &= \frac{15}{4x}&& \text{multiply ALL terms by } \color{blue}{ x\cdot4 }. \\[1 em]x\cdot4\cdot\frac{4}{x} &= x\cdot4\cdot\frac{15}{4x}&& \text{cancel out the denominators} \\[1 em]16 &= 15x^2&& \text{move all terms to the left hand side } \\[1 em]16-15x^2 &= 0&& \text{simplify left side} \\[1 em]-15x^2+16 &= 0&& \\[1 em] \end{aligned} $$
$ -15x^{2}+16 = 0 $ is a quadratic equation.
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