$$3^2 = 96237 \cdot \frac{x^4}{4000}+2219\frac{x^2}{200}+72\frac{x}{5}-\frac{551}{100}$$
Answer
$$ \begin{matrix}x_1 = 0.5735 & x_2 = -0.93366 & x_3 = 0.18008+1.0459i \\[1 em] x_4 = 0.18008-1.0459i & \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 3^2 &= 96237 \cdot \frac{x^4}{4000}+2219\frac{x^2}{200}+72\frac{x}{5}-\frac{551}{100}&& \text{multiply ALL terms by } \color{blue}{ 4000 }. \\[1 em]4000\cdot3^2 &= 4000\cdot96237 \cdot \frac{x^4}{4000}+4000\cdot2219\frac{x^2}{200}+4000\cdot72\frac{x}{5}-4000\cdot\frac{551}{100}&& \text{cancel out the denominators} \\[1 em]36000 &= 96237x^4+44380x^2+57600x-22040&& \text{move all terms to the left hand side } \\[1 em]36000-96237x^4-44380x^2-57600x+22040 &= 0&& \text{simplify left side} \\[1 em]-96237x^4-44380x^2-57600x+58040 &= 0&& \\[1 em] \end{aligned} $$
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