Question
$$5x^3-8x^2+7x+1 = 9x^3+5x^2-2$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} 5x^3-8x^2+7x+1 &= 9x^3+5x^2-2&& \text{move all terms to the left hand side } \\[1 em]5x^3-8x^2+7x+1-9x^3-5x^2+2 &= 0&& \text{simplify left side} \\[1 em]-4x^3-13x^2+7x+3 &= 0&& \\[1 em] \end{aligned} $$
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