$$\frac{1+x}{2}+\frac{3-x}{4} = 2x^3-7x+11$$
Answer
$$ \begin{matrix}x_1 = -2.38159 & x_2 = 1.19079+0.79307i & x_3 = 1.19079-0.79307i \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{1+x}{2}+\frac{3-x}{4} &= 2x^3-7x+11&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4 \cdot \frac{1+x}{2}+4\frac{3-x}{4} &= 4\cdot2x^3-4\cdot7x+4\cdot11&& \text{cancel out the denominators} \\[1 em]2x+2+3-x &= 8x^3-28x+44&& \text{simplify left side} \\[1 em]x+5 &= 8x^3-28x+44&& \text{move all terms to the left hand side } \\[1 em]x+5-8x^3+28x-44 &= 0&& \text{simplify left side} \\[1 em]-8x^3+29x-39 &= 0&& \\[1 em] \end{aligned} $$
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