Question
$$\frac{2}{9}x^3+\frac{8}{9}x^2-\frac{26}{13}x = \frac{7}{10}x+5$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} \frac{2}{9}x^3+\frac{8}{9}x^2-\frac{26}{13}x &= \frac{7}{10}x+5&& \text{multiply ALL terms by } \color{blue}{ 1170 }. \\[1 em]1170 \cdot \frac{2}{9}x^3+1170\frac{8}{9}x^2-1170\frac{26}{13}x &= 1170 \cdot \frac{7}{10}x+1170\cdot5&& \text{cancel out the denominators} \\[1 em]260x^3+1040x^2-2340x &= 819x+5850&& \text{move all terms to the left hand side } \\[1 em]260x^3+1040x^2-2340x-819x-5850 &= 0&& \text{simplify left side} \\[1 em]260x^3+1040x^2-3159x-5850 &= 0&& \\[1 em] \end{aligned} $$
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