$$8 \cdot \frac{x}{2}x+4+9x-\frac{15}{3}x+6 = 6x-\frac{7}{x}+2$$
Answer
$$ \begin{matrix}x_1 = -0.64079 & x_2 = 0.57039+1.55102i & x_3 = 0.57039-1.55102i \end{matrix} $$
Explanation
$$ \begin{aligned} 8 \cdot \frac{x}{2}x+4+9x-\frac{15}{3}x+6 &= 6x-\frac{7}{x}+2&& \text{multiply ALL terms by } \color{blue}{ 2\cdot3x }. \\[1 em]2\cdot3x8 \cdot \frac{x}{2}x+2\cdot3x\cdot4+2\cdot3x\cdot9x-2\cdot3x\frac{15}{3}x+2\cdot3x\cdot6 &= 2\cdot3x\cdot6x-2\cdot3x\cdot\frac{7}{x}+2\cdot3x\cdot2&& \text{cancel out the denominators} \\[1 em]24x^3+24x+54x^2-30x^2+36x &= 36x^2-42+12x&& \text{simplify left and right hand side} \\[1 em]24x^3+24x^2+60x &= 36x^2+12x-42&& \text{move all terms to the left hand side } \\[1 em]24x^3+24x^2+60x-36x^2-12x+42 &= 0&& \text{simplify left side} \\[1 em]24x^3-12x^2+48x+42 &= 0&& \\[1 em] \end{aligned} $$
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
Equations Solver