Chapter 1 - Section 1.4 - Radical Equations; Equations Quadratic in Form; Factorable Equations - 1.4 Assess Your Understanding - Page 118: 87

$x=\displaystyle \frac{2}{5}$

We solve by factoring with grouping: $5x^{3}+45x=2x^{2}+18$ $5x^{3}+45x-2x^{2}-18=0$ $5x^{3}-2x^{2}+45x-18=0$ $x^{2}(5x-2)+9(5x-2)=0$ $(5x-2)(x^{2}+9)=0$ $5x-2=0$ or $x^{2}+9=0$ $5x=2$ or $x^{2}=-9$ $x=\displaystyle \frac{2}{5}$ or $x=\pm \sqrt{-9}=$ not real $x=\displaystyle \frac{2}{5}$