Question
$$3x-\frac{5}{x} = 2$$
Answer
$$ \begin{matrix}x_1 = -1 & x_2 = \dfrac{ 5 }{ 3 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 3x-\frac{5}{x} &= 2&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]x\cdot3x-x\cdot\frac{5}{x} &= x\cdot2&& \text{cancel out the denominators} \\[1 em]3x^2-5 &= 2x&& \text{move all terms to the left hand side } \\[1 em]3x^2-5-2x &= 0&& \text{simplify left side} \\[1 em]3x^2-2x-5 &= 0&& \\[1 em] \end{aligned} $$
$ 3x^{2}-2x-5 = 0 $ is a quadratic equation.
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