Question
$$36x^3+86x = 4x^4-22x$$
Answer
$$ x = 0 $$
Explanation
$$ \begin{aligned} 36x^3+86x &= 4x^4-22x&& \text{move all terms to the left hand side } \\[1 em]36x^3+86x-4x^4+22x &= 0&& \text{simplify left side} \\[1 em]-4x^4+36x^3+108x &= 0&& \\[1 em] \end{aligned} $$
In order to solve $ \color{blue}{ -4x^{4}+36x^{3}+108x = 0 } $, first we need to factor our $ x $.
$$ -4x^{4}+36x^{3}+108x = x \left( -4x^{3}+36x^{2}+108 \right) $$$ x = 0 $ is a root of multiplicity $ 1 $.
The remaining roots can be found by solving equation $ -4x^{3}+36x^{2}+108 = 0$.
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using qubic formulas.
This page was created using
Polynomial Equations Solver