Question
$$8x = 6-\frac{4}{x}$$
Answer
$$ \begin{matrix}x_1 = \dfrac{ 3 }{ 8 }+\dfrac{\sqrt{ 23 }}{ 8 }i & x_2 = \dfrac{ 3 }{ 8 }-\dfrac{\sqrt{ 23 }}{ 8 }i \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 8x &= 6-\frac{4}{x}&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]x\cdot8x &= x\cdot6-x\cdot\frac{4}{x}&& \text{cancel out the denominators} \\[1 em]8x^2 &= 6x-4&& \text{move all terms to the left hand side } \\[1 em]8x^2-6x+4 &= 0&& \\[1 em] \end{aligned} $$
$ 8x^{2}-6x+4 = 0 $ is a quadratic equation.
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