$$x^4+20x^2+100x = 0$$
Answer
$$ \begin{matrix}x_1 = 0 & x_2 = -3.26297 & x_3 = 1.63148+5.29011i \\[1 em] x_4 = 1.63148-5.29011i & \\[1 em] \end{matrix} $$
Explanation
In order to solve $ \color{blue}{ x^{4}+20x^{2}+100x = 0 } $, first we need to factor our $ x $.
$$ x^{4}+20x^{2}+100x = x \left( x^{3}+20x+100 \right) $$$ x = 0 $ is a root of multiplicity $ 1 $.
The remaining roots can be found by solving equation $ x^{3}+20x+100 = 0$.
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using qubic formulas.
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