$$5x^3+6x^2-7x+8 = 4+x$$
Answer
$$ \begin{matrix}x_1 = -2.12836 & x_2 = 0.46418+0.40052i & x_3 = 0.46418-0.40052i \end{matrix} $$
Explanation
$$ \begin{aligned} 5x^3+6x^2-7x+8 &= 4+x&& \text{move all terms to the left hand side } \\[1 em]5x^3+6x^2-7x+8-4-x &= 0&& \text{simplify left side} \\[1 em]5x^3+6x^2-8x+4 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using qubic formulas.
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Polynomial Equations Solver