Question
$$9x^2-3x^3 = -x^2+3x+8$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} 9x^2-3x^3 &= -x^2+3x+8&& \text{simplify left side} \\[1 em]-3x^3+9x^2 &= -x^2+3x+8&& \text{move all terms to the left hand side } \\[1 em]-3x^3+9x^2+x^2-3x-8 &= 0&& \text{simplify left side} \\[1 em]-3x^3+10x^2-3x-8 &= 0&& \\[1 em] \end{aligned} $$
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