$$2a-\frac{6}{a} = a$$
Answer
$$ \begin{matrix}a_1 = -\sqrt{ 6 } & a_2 = \sqrt{ 6 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 2a-\frac{6}{a} &= a&& \text{multiply ALL terms by } \color{blue}{ a }. \\[1 em]a\cdot2a-a\cdot\frac{6}{a} &= aa&& \text{cancel out the denominators} \\[1 em]2a^2-6 &= a^2&& \text{move all terms to the left hand side } \\[1 em]2a^2-6-a^2 &= 0&& \text{simplify left side} \\[1 em]a^2-6 &= 0&& \\[1 em] \end{aligned} $$
$ x^{2}-6 = 0 $ is a quadratic equation.
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