$$\frac{4x+5+14x^2-4x^3}{2+2x+4x^2} = 0$$
Answer
$$ \begin{matrix}x_1 = 3.84467 & x_2 = -0.17233+0.54353i & x_3 = -0.17233-0.54353i \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{4x+5+14x^2-4x^3}{2+2x+4x^2} &= 0&& \text{multiply ALL terms by } \color{blue}{ 2+2x+4x^2 }. \\[1 em](2+2x+4x^2)\frac{4x+5+14x^2-4x^3}{2+2x+4x^2} &= (2+2x+4x^2)\cdot0&& \text{cancel out the denominators} \\[1 em]4x+5+14x^2-4x^3 &= 0&& \text{simplify left side} \\[1 em]-4x^3+14x^2+4x+5 &= 0&& \\[1 em] \end{aligned} $$
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