$$\frac{1+x}{2}+\frac{3-x}{4} = x^3-x$$
Answer
$$ \begin{matrix}x_1 = 1.45274 & x_2 = -0.72637+0.57692i & x_3 = -0.72637-0.57692i \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{1+x}{2}+\frac{3-x}{4} &= x^3-x&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4 \cdot \frac{1+x}{2}+4\frac{3-x}{4} &= 4x^3-4x&& \text{cancel out the denominators} \\[1 em]2x+2+3-x &= 4x^3-4x&& \text{simplify left side} \\[1 em]x+5 &= 4x^3-4x&& \text{move all terms to the left hand side } \\[1 em]x+5-4x^3+4x &= 0&& \text{simplify left side} \\[1 em]-4x^3+5x+5 &= 0&& \\[1 em] \end{aligned} $$
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