Question
$$8x^3+8-(x^3-2) = 0$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} 8x^3+8-(x^3-2) &= 0&& \text{simplify left side} \\[1 em]8x^3+8-x^3+2 &= 0&& \\[1 em]7x^3+10 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using qubic formulas.
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