Question
$$x^5+3x^5-4x\cdot2+10 = x+2$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} x^5+3x^5-4x\cdot2+10 &= x+2&& \text{simplify left side} \\[1 em]x^5+3x^5-8x+10 &= x+2&& \\[1 em]4x^5-8x+10 &= x+2&& \text{move all terms to the left hand side } \\[1 em]4x^5-8x+10-x-2 &= 0&& \text{simplify left side} \\[1 em]4x^5-9x+8 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using Newton method.
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Polynomial Equations Solver