$$\frac{1+x}{2}+\frac{3-x}{4} = x(x+3)(x-1)(2x+3)$$
Answer
$$ \begin{matrix}x_1 = -0.13701 & x_2 = -1.41742 & x_3 = 1.06799 \\[1 em] x_4 = -3.01356 & \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{1+x}{2}+\frac{3-x}{4} &= x(x+3)(x-1)(2x+3)&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4 \cdot \frac{1+x}{2}+4\frac{3-x}{4} &= 4x(x+3)(x-1)(2x+3)&& \text{cancel out the denominators} \\[1 em]2x+2+3-x &= 8x^4+28x^3-36x&& \text{simplify left side} \\[1 em]x+5 &= 8x^4+28x^3-36x&& \text{move all terms to the left hand side } \\[1 em]x+5-8x^4-28x^3+36x &= 0&& \text{simplify left side} \\[1 em]-8x^4-28x^3+37x+5 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using quartic formulas
This page was created using
Equations Solver