$$x+1 = (2x+5)^4$$
Answer
$$ \begin{matrix}x_1 = -2.10709+0.33854i & x_2 = -2.10709-0.33854i & x_3 = -2.89291+0.44062i \\[1 em] x_4 = -2.89291-0.44062i & \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} x+1 &= (2x+5)^4&& \text{simplify right side} \\[1 em]x+1 &= 16x^4+160x^3+600x^2+1000x+625&& \text{move all terms to the left hand side } \\[1 em]x+1-16x^4-160x^3-600x^2-1000x-625 &= 0&& \text{simplify left side} \\[1 em]-16x^4-160x^3-600x^2-999x-624 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using quartic formulas
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