$$3x+\frac{4}{x^2}+4x-5 = 0$$
Answer
$$ \begin{matrix}x_1 = -0.64773 & x_2 = 0.68101+0.64687i & x_3 = 0.68101-0.64687i \end{matrix} $$
Explanation
$$ \begin{aligned} 3x+\frac{4}{x^2}+4x-5 &= 0&& \text{multiply ALL terms by } \color{blue}{ x^2 }. \\[1 em]x^2\cdot3x+x^2\cdot\frac{4}{x^2}+x^2\cdot4x-x^2\cdot5 &= x^2\cdot0&& \text{cancel out the denominators} \\[1 em]3x^3+4+4x^3-5x^2 &= 0&& \text{simplify left side} \\[1 em]7x^3-5x^2+4 &= 0&& \\[1 em] \end{aligned} $$
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