Question
$$x^3-2x^2-19x+\frac{20}{x}-5 = 0$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} x^3-2x^2-19x+\frac{20}{x}-5 &= 0&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]xx^3-x\cdot2x^2-x\cdot19x+x\cdot\frac{20}{x}-x\cdot5 &= x\cdot0&& \text{cancel out the denominators} \\[1 em]x^4-2x^3-19x^2+20-5x &= 0&& \text{simplify left side} \\[1 em]x^4-2x^3-19x^2-5x+20 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using quartic formulas
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