Question
$$2-\frac{3}{x}+6 = x+\frac{2}{x}+6$$
Answer
$$ \begin{matrix}x_1 = 1+2i & x_2 = 1-2i \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 2-\frac{3}{x}+6 &= x+\frac{2}{x}+6&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]x\cdot2-x\cdot\frac{3}{x}+x\cdot6 &= xx+x\cdot\frac{2}{x}+x\cdot6&& \text{cancel out the denominators} \\[1 em]2x-3+6x &= x^2+2+6x&& \text{simplify left and right hand side} \\[1 em]8x-3 &= x^2+6x+2&& \text{move all terms to the left hand side } \\[1 em]8x-3-x^2-6x-2 &= 0&& \text{simplify left side} \\[1 em]-x^2+2x-5 &= 0&& \\[1 em] \end{aligned} $$
$ -x^{2}+2x-5 = 0 $ is a quadratic equation.
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