$$10000 = \frac{1873}{10}x^4-\frac{1260}{1}x^3+\frac{35663}{10}x^2-\frac{35953}{10}x+\frac{46542}{10}$$
Answer
$$ \begin{matrix}x_1 = -0.75459 & x_2 = 3.52171 & x_3 = 1.98003+2.61143i \\[1 em] x_4 = 1.98003-2.61143i & \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 10000 &= \frac{1873}{10}x^4-\frac{1260}{1}x^3+\frac{35663}{10}x^2-\frac{35953}{10}x+\frac{46542}{10}&& \text{multiply ALL terms by } \color{blue}{ 10 }. \\[1 em]10\cdot10000 &= 10 \cdot \frac{1873}{10}x^4-10\frac{1260}{1}x^3+10\frac{35663}{10}x^2-10\frac{35953}{10}x+10\cdot\frac{46542}{10}&& \text{cancel out the denominators} \\[1 em]100000 &= 1873x^4-12600x^3+35663x^2-35953x+46542&& \text{move all terms to the left hand side } \\[1 em]100000-1873x^4+12600x^3-35663x^2+35953x-46542 &= 0&& \text{simplify left side} \\[1 em]-1873x^4+12600x^3-35663x^2+35953x+53458 &= 0&& \\[1 em] \end{aligned} $$
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