Question
$$2-\frac{9}{x}-\frac{5}{x^2} = 0$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} 2-\frac{9}{x}-\frac{5}{x^2} &= 0&& \text{multiply ALL terms by } \color{blue}{ xx^2 }. \\[1 em]xx^2\cdot2-xx^2\cdot\frac{9}{x}-xx^2\cdot\frac{5}{x^2} &= xx^2\cdot0&& \text{cancel out the denominators} \\[1 em]2x^3-9-\frac{5}{x^1} &= 0&& \text{multiply ALL terms by } \color{blue}{ x^1 }. \\[1 em]x^1\cdot2x^3-x^1\cdot9-x^1\cdot\frac{5}{x^1} &= x^1\cdot0&& \text{cancel out the denominators} \\[1 em]2x^4-9x-5 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using quartic formulas
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