$$\frac{1}{x} = 2x-\frac{4}{6}x$$
Answer
$$ \begin{matrix}x_1 = - \dfrac{\sqrt{ 3 }}{ 2 } & x_2 = \dfrac{\sqrt{ 3 }}{ 2 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{1}{x} &= 2x-\frac{4}{6}x&& \text{multiply ALL terms by } \color{blue}{ x\cdot6 }. \\[1 em]x\cdot6\cdot\frac{1}{x} &= x\cdot6\cdot2x-x\cdot6 \cdot \frac{4}{6}x&& \text{cancel out the denominators} \\[1 em]6 &= 12x^2-4x^2&& \text{simplify right side} \\[1 em]6 &= 8x^2&& \text{move all terms to the left hand side } \\[1 em]6-8x^2 &= 0&& \text{simplify left side} \\[1 em]-8x^2+6 &= 0&& \\[1 em] \end{aligned} $$
$ -8x^{2}+6 = 0 $ is a quadratic equation.
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