# Chapter 8 - Mid-Chapter Check Point - Page 629: 12

$x = \frac{-3±\sqrt{41}}{4}$

#### Work Step by Step

$\frac{x^2}{3} + \frac{x}{2} = \frac{2}{3}$ Multiply the equation by the least common multiple $6$. $\frac{x^2}{3}⋅6 + \frac{x}{2}⋅6 = \frac{2}{3}⋅6$ $2x^2+3x = 4$ $2x^2+3x-4 = 0$ Use the quadratic formula: $x = \frac{-b±\sqrt{b^2-4ac}}{2a}$ $a=2$, $b=3$, $c=-4$ $x = \frac{-3±\sqrt{3^2-(4⋅2⋅-4)}}{(2⋅2)}$ $x = \frac{-3±\sqrt{9-(-32)}}{4}$ $x = \frac{-3±\sqrt{41}}{4}$

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