$$\frac{1}{x}-2 = \frac{x}{8}$$
Answer
$$ \begin{matrix}x_1 = -8-6 \sqrt{ 2 } & x_2 = -8+6 \sqrt{ 2 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{1}{x}-2 &= \frac{x}{8}&& \text{multiply ALL terms by } \color{blue}{ x\cdot8 }. \\[1 em]x\cdot8\cdot\frac{1}{x}-x\cdot8\cdot2 &= x\cdot8 \cdot \frac{x}{8}&& \text{cancel out the denominators} \\[1 em]8-16x &= x^2&& \text{move all terms to the left hand side } \\[1 em]8-16x-x^2 &= 0&& \text{simplify left side} \\[1 em]-x^2-16x+8 &= 0&& \\[1 em] \end{aligned} $$
$ -x^{2}-16x+8 = 0 $ is a quadratic equation.
You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this equation.
This page was created using
Equations Solver