$$x\cdot2-x-\frac{6}{x}+2 = 0$$
Answer
$$ \begin{matrix}x_1 = -1-\sqrt{ 7 } & x_2 = -1+\sqrt{ 7 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} x\cdot2-x-\frac{6}{x}+2 &= 0&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]xx\cdot2-xx-x\cdot\frac{6}{x}+x\cdot2 &= x\cdot0&& \text{cancel out the denominators} \\[1 em]2x^2-x^2-6+2x &= 0&& \text{simplify left side} \\[1 em]x^2+2x-6 &= 0&& \\[1 em] \end{aligned} $$
$ x^{2}+2x-6 = 0 $ is a quadratic equation.
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