Question
$$-\frac{1}{3}x-5 = \frac{3}{x}-35$$
Answer
$$ \begin{matrix}x_1 = 45-12 \sqrt{ 14 } & x_2 = 45+12 \sqrt{ 14 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} -\frac{1}{3}x-5 &= \frac{3}{x}-35&& \text{multiply ALL terms by } \color{blue}{ 3x }. \\[1 em]-3x \cdot \frac{1}{3}x-3x\cdot5 &= 3x\cdot\frac{3}{x}-3x\cdot35&& \text{cancel out the denominators} \\[1 em]-x^2-15x &= 9-105x&& \text{move all terms to the left hand side } \\[1 em]-x^2-15x-9+105x &= 0&& \text{simplify left side} \\[1 em]-x^2+90x-9 &= 0&& \\[1 em] \end{aligned} $$
$ -x^{2}+90x-9 = 0 $ is a quadratic equation.
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