Question
$$\frac{4}{x}-3 = x$$
Answer
$$ \begin{matrix}x_1 = 1 & x_2 = -4 \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{4}{x}-3 &= x&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]x\cdot\frac{4}{x}-x\cdot3 &= xx&& \text{cancel out the denominators} \\[1 em]4-3x &= x^2&& \text{move all terms to the left hand side } \\[1 em]4-3x-x^2 &= 0&& \text{simplify left side} \\[1 em]-x^2-3x+4 &= 0&& \\[1 em] \end{aligned} $$
$ -x^{2}-3x+4 = 0 $ is a quadratic equation.
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