Question
$$84^3 = 2x^3+3x^2+x$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} 84^3 &= 2x^3+3x^2+x&& \text{simplify left side} \\[1 em]592704 &= 2x^3+3x^2+x&& \text{move all terms to the left hand side } \\[1 em]592704-2x^3-3x^2-x &= 0&& \text{simplify left side} \\[1 em]-2x^3-3x^2-x+592704 &= 0&& \\[1 em] \end{aligned} $$
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