Question
$$2x-x-13x-\frac{6}{x}-3 = 0$$
Answer
$$ \begin{matrix}x_1 = -\dfrac{ 1 }{ 8 }+\dfrac{\sqrt{ 31 }}{ 8 }i & x_2 = -\dfrac{ 1 }{ 8 }-\dfrac{\sqrt{ 31 }}{ 8 }i \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 2x-x-13x-\frac{6}{x}-3 &= 0&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]x\cdot2x-xx-x\cdot13x-x\cdot\frac{6}{x}-x\cdot3 &= x\cdot0&& \text{cancel out the denominators} \\[1 em]2x^2-x^2-13x^2-6-3x &= 0&& \text{simplify left side} \\[1 em]-12x^2-3x-6 &= 0&& \\[1 em] \end{aligned} $$
$ -12x^{2}-3x-6 = 0 $ is a quadratic equation.
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