Question
$$-10x^2+20x+\frac{80}{x}+2 = 0$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} -10x^2+20x+\frac{80}{x}+2 &= 0&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]-x\cdot10x^2+x\cdot20x+x\cdot\frac{80}{x}+x\cdot2 &= x\cdot0&& \text{cancel out the denominators} \\[1 em]-10x^3+20x^2+80+2x &= 0&& \text{simplify left side} \\[1 em]-10x^3+20x^2+2x+80 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using qubic formulas.
This page was created using
Polynomial Equations Solver