$$50x+\frac{6144}{x^2} = 0$$
Answer
$$ \begin{matrix}x_1 = -4.97157 & x_2 = 2.48579+4.30551i & x_3 = 2.48579-4.30551i \end{matrix} $$
Explanation
$$ \begin{aligned} 50x+\frac{6144}{x^2} &= 0&& \text{multiply ALL terms by } \color{blue}{ x^2 }. \\[1 em]x^2\cdot50x+x^2\cdot\frac{6144}{x^2} &= x^2\cdot0&& \text{cancel out the denominators} \\[1 em]50x^3+6144 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using qubic formulas.
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