$$x(\frac{2500}{371}-\frac{30}{x}) = 189$$
Answer
$$ \begin{matrix}x_1 = 0 & x_2 = 5.41022 & x_3 = -0.47911+2.2259i \\[1 em] x_4 = -0.47911-2.2259i & \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} x(\frac{2500}{371}-\frac{30}{x}) &= 189&& \text{simplify left side} \\[1 em]x \cdot \frac{2500x-11130}{371x} &= 189&& \\[1 em]\frac{2500x^2-11130x}{371x} &= 189&& \text{multiply ALL terms by } \color{blue}{ 371x }. \\[1 em]371x \cdot \frac{2500x^2-11130x}{371x} &= 371x\cdot189&& \text{cancel out the denominators} \\[1 em]2500x^4-11130x^3 &= 70119x&& \text{move all terms to the left hand side } \\[1 em]2500x^4-11130x^3-70119x &= 0&& \\[1 em] \end{aligned} $$
In order to solve $ \color{blue}{ 2500x^{4}-11130x^{3}-70119x = 0 } $, first we need to factor our $ x $.
$$ 2500x^{4}-11130x^{3}-70119x = x \left( 2500x^{3}-11130x^{2}-70119 \right) $$$ x = 0 $ is a root of multiplicity $ 1 $.
The remaining roots can be found by solving equation $ 2500x^{3}-11130x^{2}-70119 = 0$.
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using qubic formulas.
This page was created using
Polynomial Equations Solver