$$\frac{4}{3}x^3+\frac{914}{100}x^2-0x-12727 = 0$$
Answer
$$ \begin{matrix}x_1 = 19.15633 & x_2 = -13.00567+18.14206i & x_3 = -13.00567-18.14206i \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{4}{3}x^3+\frac{914}{100}x^2-0x-12727 &= 0&& \text{multiply ALL terms by } \color{blue}{ 300 }. \\[1 em]300 \cdot \frac{4}{3}x^3+300\frac{914}{100}x^2-300\cdot0x-300\cdot12727 &= 300\cdot0&& \text{cancel out the denominators} \\[1 em]400x^3+2742x^2-0-3818100 &= 0&& \text{simplify left side} \\[1 em]400x^3+2742x^2-0-3818100 &= 0&& \\[1 em]400x^3+2742x^2-3818100 &= 0&& \\[1 em] \end{aligned} $$
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