$$-x^4+\frac{6}{5}x^3-\frac{3}{5}x^2+\frac{1}{10}x-\frac{1}{80} = 0$$
Answer
$$ \begin{matrix}x_1 = 0.08575+0.15671i & x_2 = 0.08575-0.15671i & x_3 = 0.51425+0.35671i \\[1 em] x_4 = 0.51425-0.35671i & \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} -x^4+\frac{6}{5}x^3-\frac{3}{5}x^2+\frac{1}{10}x-\frac{1}{80} &= 0&& \text{multiply ALL terms by } \color{blue}{ 80 }. \\[1 em]-80x^4+80 \cdot \frac{6}{5}x^3-80\frac{3}{5}x^2+80\frac{1}{10}x-80\cdot\frac{1}{80} &= 80\cdot0&& \text{cancel out the denominators} \\[1 em]-80x^4+96x^3-48x^2+8x-1 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using quartic formulas
This page was created using
Polynomial Equations Solver