$$3x-\frac{4}{10} = \frac{3}{2}x^2+3x^3$$
Answer
$$ \begin{matrix}x_1 = 0.1474 & x_2 = 0.68097 & x_3 = -1.32837 \end{matrix} $$
Explanation
$$ \begin{aligned} 3x-\frac{4}{10} &= \frac{3}{2}x^2+3x^3&& \text{multiply ALL terms by } \color{blue}{ 10 }. \\[1 em]10\cdot3x-10\cdot\frac{4}{10} &= 10 \cdot \frac{3}{2}x^2+10\cdot3x^3&& \text{cancel out the denominators} \\[1 em]30x-4 &= 15x^2+30x^3&& \text{simplify right side} \\[1 em]30x-4 &= 30x^3+15x^2&& \text{move all terms to the left hand side } \\[1 em]30x-4-30x^3-15x^2 &= 0&& \text{simplify left side} \\[1 em]-30x^3-15x^2+30x-4 &= 0&& \\[1 em] \end{aligned} $$
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