Question
$$x^2+4x+\frac{250000}{x^3} = 0$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} x^2+4x+\frac{250000}{x^3} &= 0&& \text{multiply ALL terms by } \color{blue}{ x^3 }. \\[1 em]x^3x^2+x^3\cdot4x+x^3\cdot\frac{250000}{x^3} &= x^3\cdot0&& \text{cancel out the denominators} \\[1 em]x^5+4x^4+250000 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using Newton method.
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