How do you solve 6-2x^2=9x+15 using the quadratic formula?

1 Answer
Jul 27, 2017

$x = - 3$

$x = - \frac{3}{2}$

Explanation:

Get all the terms on the left side and rearrange:

$- 2 {x}^{2} - 9 x - 9 = 0$

Apply the quadratic formula knowing $a = - 2 , b = - 9 , c = - 9$:

${x}_{1 , 2} = \frac{- \left(- 9\right) \pm \sqrt{{\left(- 9\right)}^{2} - 4 \cdot \left(- 2\right) \cdot \left(- 9\right)}}{2 \cdot \left(- 2\right)}$

${x}_{1 , 2} = \frac{9 \pm \sqrt{81 - 72}}{-} 4 = \frac{9 \pm 3}{-} 4 \implies \left\{\begin{matrix}{x}_{1} = \frac{12}{-} 4 = - 3 \\ {x}_{2} = \frac{6}{-} 4 = - \frac{3}{2}\end{matrix}\right.$