Question
$$4-x = \frac{15}{x}$$
Answer
$$ \begin{matrix}x_1 = 2+\sqrt{ 11 }i & x_2 = 2-\sqrt{ 11 }i \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 4-x &= \frac{15}{x}&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]x\cdot4-xx &= x\cdot\frac{15}{x}&& \text{cancel out the denominators} \\[1 em]4x-x^2 &= 15&& \text{simplify left side} \\[1 em]-x^2+4x &= 15&& \text{move all terms to the left hand side } \\[1 em]-x^2+4x-15 &= 0&& \\[1 em] \end{aligned} $$
$ -x^{2}+4x-15 = 0 $ is a quadratic equation.
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