$$6x-\frac{1}{x^2}-1 = 0$$
Answer
$$ \begin{matrix}x_1 = 0.61186 & x_2 = -0.2226+0.47206i & x_3 = -0.2226-0.47206i \end{matrix} $$
Explanation
$$ \begin{aligned} 6x-\frac{1}{x^2}-1 &= 0&& \text{multiply ALL terms by } \color{blue}{ x^2 }. \\[1 em]x^2\cdot6x-x^2\cdot\frac{1}{x^2}-x^2\cdot1 &= x^2\cdot0&& \text{cancel out the denominators} \\[1 em]6x^3-1-x^2 &= 0&& \text{simplify left side} \\[1 em]6x^3-x^2-1 &= 0&& \\[1 em] \end{aligned} $$
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
Equations Solver