Question
$$120 = 16 \cdot \frac{x}{9}x$$
Answer
$$ \begin{matrix}x_1 = -3 \dfrac{\sqrt{ 30 }}{ 2 } & x_2 = \dfrac{ 3 \sqrt{ 30}}{ 2 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 120 &= 16 \cdot \frac{x}{9}x&& \text{multiply ALL terms by } \color{blue}{ 9 }. \\[1 em]9\cdot120 &= 916 \cdot \frac{x}{9}x&& \text{cancel out the denominators} \\[1 em]1080 &= 16x^2&& \text{move all terms to the left hand side } \\[1 em]1080-16x^2 &= 0&& \text{simplify left side} \\[1 em]-16x^2+1080 &= 0&& \\[1 em] \end{aligned} $$
$ -16x^{2}+1080 = 0 $ is a quadratic equation.
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