$$\frac{a^3}{3}-2a-\frac{2}{3} = 0$$
Answer
$$ \begin{matrix}a_1 = -0.33988 & a_2 = -2.2618 & a_3 = 2.60168 \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{a^3}{3}-2a-\frac{2}{3} &= 0&& \text{multiply ALL terms by } \color{blue}{ 3 }. \\[1 em]3 \cdot \frac{a^3}{3}-3\cdot2a-3\cdot\frac{2}{3} &= 3\cdot0&& \text{cancel out the denominators} \\[1 em]a^3-6a-2 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using qubic formulas.
This page was created using
Polynomial Equations Solver