Question
$$3x-\frac{1}{2}-\frac{1}{x} = 0$$
Answer
$$ \begin{matrix}x_1 = -\dfrac{ 1 }{ 2 } & x_2 = \dfrac{ 2 }{ 3 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 3x-\frac{1}{2}-\frac{1}{x} &= 0&& \text{multiply ALL terms by } \color{blue}{ 2x }. \\[1 em]2x\cdot3x-2x\cdot\frac{1}{2}-2x\cdot\frac{1}{x} &= 2x\cdot0&& \text{cancel out the denominators} \\[1 em]6x^2-x-2 &= 0&& \\[1 em] \end{aligned} $$
$ 6x^{2}-x-2 = 0 $ is a quadratic equation.
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