Question
$$x^2+5x^2+5x-\frac{3}{x}+3 = 0$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} x^2+5x^2+5x-\frac{3}{x}+3 &= 0&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]xx^2+x\cdot5x^2+x\cdot5x-x\cdot\frac{3}{x}+x\cdot3 &= x\cdot0&& \text{cancel out the denominators} \\[1 em]x^3+5x^3+5x^2-3+3x &= 0&& \text{simplify left side} \\[1 em]6x^3+5x^2+3x-3 &= 0&& \\[1 em] \end{aligned} $$
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