Question
$$\frac{5}{2}x^2+\frac{1}{10}x^3+\frac{1789}{200}x = \frac{822}{25}$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} \frac{5}{2}x^2+\frac{1}{10}x^3+\frac{1789}{200}x &= \frac{822}{25}&& \text{multiply ALL terms by } \color{blue}{ 200 }. \\[1 em]200 \cdot \frac{5}{2}x^2+200\frac{1}{10}x^3+200\frac{1789}{200}x &= 200\cdot\frac{822}{25}&& \text{cancel out the denominators} \\[1 em]500x^2+20x^3+1789x &= 6576&& \text{simplify left side} \\[1 em]20x^3+500x^2+1789x &= 6576&& \text{move all terms to the left hand side } \\[1 em]20x^3+500x^2+1789x-6576 &= 0&& \\[1 em] \end{aligned} $$
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