$$\frac{1}{2}x+3x^4 = 3x-\frac{4}{10}$$
Answer
$$ \begin{matrix}x_1 = 0.1608 & x_2 = 0.88016 & x_3 = -0.52048+0.81925i \\[1 em] x_4 = -0.52048-0.81925i & \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{1}{2}x+3x^4 &= 3x-\frac{4}{10}&& \text{multiply ALL terms by } \color{blue}{ 10 }. \\[1 em]10 \cdot \frac{1}{2}x+10\cdot3x^4 &= 10\cdot3x-10\cdot\frac{4}{10}&& \text{cancel out the denominators} \\[1 em]5x+30x^4 &= 30x-4&& \text{simplify left side} \\[1 em]30x^4+5x &= 30x-4&& \text{move all terms to the left hand side } \\[1 em]30x^4+5x-30x+4 &= 0&& \text{simplify left side} \\[1 em]30x^4-25x+4 &= 0&& \\[1 em] \end{aligned} $$
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