How do you solve x(2x + 3) = 9?

Apr 15, 2016

-3 and $\frac{3}{2}$

Explanation:

Bring the equation to standard form:
$y = 2 {x}^{2} + 3 x - 9 = 0$
Use the improved quadratic formula to solve this equation.
$D = {d}^{2} = {b}^{2} - 4 a c = 9 + 72 = 81$ ---> $d = \pm 9$
There are 2 real roots:
$x = - \frac{b}{2 a} \pm \frac{d}{2 a} = - \frac{3}{4} \pm \frac{9}{4} = \frac{- 3 \pm 9}{4}$
$x = - \frac{12}{4} = - 3$
$x = \frac{6}{4} = \frac{3}{2}$