$$2a^2-\frac{6}{a} = a$$
Answer
$$ \begin{matrix}a_1 = 1.62964 & a_2 = -0.56482+1.23364i & a_3 = -0.56482-1.23364i \end{matrix} $$
Explanation
$$ \begin{aligned} 2a^2-\frac{6}{a} &= a&& \text{multiply ALL terms by } \color{blue}{ a }. \\[1 em]a\cdot2a^2-a\cdot\frac{6}{a} &= aa&& \text{cancel out the denominators} \\[1 em]2a^3-6 &= a^2&& \text{move all terms to the left hand side } \\[1 em]2a^3-6-a^2 &= 0&& \text{simplify left side} \\[1 em]2a^3-a^2-6 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using qubic formulas.
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