$$8v^2+2+3v^2+6v^3-(2v^2-8v^3) = 0$$
Answer
$$ \begin{matrix}v_1 = -0.8436 & v_2 = 0.10037+0.39909i & v_3 = 0.10037-0.39909i \end{matrix} $$
Explanation
$$ \begin{aligned} 8v^2+2+3v^2+6v^3-(2v^2-8v^3) &= 0&& \text{simplify left side} \\[1 em]6v^3+11v^2+2-(2v^2-8v^3) &= 0&& \\[1 em]6v^3+11v^2+2-2v^2+8v^3 &= 0&& \\[1 em]14v^3+9v^2+2 &= 0&& \\[1 em] \end{aligned} $$
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