$$\frac{1}{2}x+3x^3 = 3x-\frac{4}{10}$$
Answer
$$ \begin{matrix}x_1 = 0.16543 & x_2 = 0.81884 & x_3 = -0.98427 \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{1}{2}x+3x^3 &= 3x-\frac{4}{10}&& \text{multiply ALL terms by } \color{blue}{ 10 }. \\[1 em]10 \cdot \frac{1}{2}x+10\cdot3x^3 &= 10\cdot3x-10\cdot\frac{4}{10}&& \text{cancel out the denominators} \\[1 em]5x+30x^3 &= 30x-4&& \text{simplify left side} \\[1 em]30x^3+5x &= 30x-4&& \text{move all terms to the left hand side } \\[1 em]30x^3+5x-30x+4 &= 0&& \text{simplify left side} \\[1 em]30x^3-25x+4 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using qubic formulas.
This page was created using
Polynomial Equations Solver