In order to solve $ \color{blue}{ 8x^{4}-5x = 0 } $, first we need to factor our $ x $.
$$ 8x^{4}-5x = x \left( 8x^{3}-5 \right) $$$ x = 0 $ is a root of multiplicity $ 1 $.
The remaining roots can be found by solving equation $ 8x^{3}-5 = 0$.
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using qubic formulas.