$$15x-\frac{20}{x^2}+3 = 0$$
Answer
$$ \begin{matrix}x_1 = 1.03785 & x_2 = -0.61893+0.94955i & x_3 = -0.61893-0.94955i \end{matrix} $$
Explanation
$$ \begin{aligned} 15x-\frac{20}{x^2}+3 &= 0&& \text{multiply ALL terms by } \color{blue}{ x^2 }. \\[1 em]x^2\cdot15x-x^2\cdot\frac{20}{x^2}+x^2\cdot3 &= x^2\cdot0&& \text{cancel out the denominators} \\[1 em]15x^3-20+3x^2 &= 0&& \text{simplify left side} \\[1 em]15x^3+3x^2-20 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using qubic formulas.
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