Question
$$4x^5+9x^3+11-(x^4+7x^3+10) = 0$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} 4x^5+9x^3+11-(x^4+7x^3+10) &= 0&& \text{simplify left side} \\[1 em]4x^5+9x^3+11-x^4-7x^3-10 &= 0&& \\[1 em]4x^5-x^4+2x^3+1 &= 0&& \\[1 em] \end{aligned} $$
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