Question
$$\frac{1+x}{2}+\frac{3-x}{4} = -6x^4+3x^3+5x^2-7x+1$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} \frac{1+x}{2}+\frac{3-x}{4} &= -6x^4+3x^3+5x^2-7x+1&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4 \cdot \frac{1+x}{2}+4\frac{3-x}{4} &= -4\cdot6x^4+4\cdot3x^3+4\cdot5x^2-4\cdot7x+4\cdot1&& \text{cancel out the denominators} \\[1 em]2x+2+3-x &= -24x^4+12x^3+20x^2-28x+4&& \text{simplify left side} \\[1 em]x+5 &= -24x^4+12x^3+20x^2-28x+4&& \text{move all terms to the left hand side } \\[1 em]x+5+24x^4-12x^3-20x^2+28x-4 &= 0&& \text{simplify left side} \\[1 em]24x^4-12x^3-20x^2+29x+1 &= 0&& \\[1 em] \end{aligned} $$
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
Polynomial Equations Solver