$$\frac{1+x}{2}+\frac{3-x}{4} = 7x-3-9x^2+x^3$$
Answer
$$ \begin{matrix}x_1 = 8.24373 & x_2 = 0.37813+0.61038i & x_3 = 0.37813-0.61038i \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{1+x}{2}+\frac{3-x}{4} &= 7x-3-9x^2+x^3&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4 \cdot \frac{1+x}{2}+4\frac{3-x}{4} &= 4\cdot7x-4\cdot3-4\cdot9x^2+4x^3&& \text{cancel out the denominators} \\[1 em]2x+2+3-x &= 28x-12-36x^2+4x^3&& \text{simplify left and right hand side} \\[1 em]x+5 &= 4x^3-36x^2+28x-12&& \text{move all terms to the left hand side } \\[1 em]x+5-4x^3+36x^2-28x+12 &= 0&& \text{simplify left side} \\[1 em]-4x^3+36x^2-27x+17 &= 0&& \\[1 em] \end{aligned} $$
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