Question
$$x \cdot \frac{x+5}{4}x+4 = \frac{9}{5}$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} x \cdot \frac{x+5}{4}x+4 &= \frac{9}{5}&& \text{multiply ALL terms by } \color{blue}{ 20 }. \\[1 em]20x \cdot \frac{x+5}{4}x+20\cdot4 &= 20\cdot\frac{9}{5}&& \text{cancel out the denominators} \\[1 em]5x^3+25x^2+80 &= 36&& \text{move all terms to the left hand side } \\[1 em]5x^3+25x^2+80-36 &= 0&& \text{simplify left side} \\[1 em]5x^3+25x^2+44 &= 0&& \\[1 em] \end{aligned} $$
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