$$\frac{1+x}{2}+\frac{3-x}{4} = 2x^3+12x^2+18x$$
Answer
$$ \begin{matrix}x_1 = 0.06732 & x_2 = -3.03366+0.2835i & x_3 = -3.03366-0.2835i \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{1+x}{2}+\frac{3-x}{4} &= 2x^3+12x^2+18x&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4 \cdot \frac{1+x}{2}+4\frac{3-x}{4} &= 4\cdot2x^3+4\cdot12x^2+4\cdot18x&& \text{cancel out the denominators} \\[1 em]2x+2+3-x &= 8x^3+48x^2+72x&& \text{simplify left side} \\[1 em]x+5 &= 8x^3+48x^2+72x&& \text{move all terms to the left hand side } \\[1 em]x+5-8x^3-48x^2-72x &= 0&& \text{simplify left side} \\[1 em]-8x^3-48x^2-71x+5 &= 0&& \\[1 em] \end{aligned} $$
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