# How do you factor and solve 9x^2 + 7x - 56 = 0?

Jul 4, 2016

(-7 +- sqrt2065)/18

#### Explanation:

$f \left(x\right) = 9 {x}^{2} + 7 x - 56 = 0$
$D = {d}^{2} = {b}^{2} - 4 a c = 49 + 2016 = 2065$
Since D is not a perfect square, this function can't be factored.
Solve f(x) = 0 by the improved quadratic formula.
$D = 2065$ --> $d = \pm \sqrt{2065}$
There are 2 real roots:
$x = - \frac{b}{2 a} \pm \frac{d}{2 a} = - \frac{7}{18} \pm \frac{\sqrt{2065}}{18} = \frac{- 7 \pm \sqrt{2065}}{18}$