Question
$$-2+x^3 = x^2+6+x$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} -2+x^3 &= x^2+6+x&& \text{simplify left and right hand side} \\[1 em]x^3-2 &= x^2+x+6&& \text{move all terms to the left hand side } \\[1 em]x^3-2-x^2-x-6 &= 0&& \text{simplify left side} \\[1 em]x^3-x^2-x-8 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using qubic formulas.
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Equations Solver