# How do you find the zeros of  y = -9x^2 + 18x -2  using the quadratic formula?

Jul 10, 2016

(3 +- sqrt7)/3

#### Explanation:

Use the improved quadratic formula (Google Search)
$y = - 9 {x}^{2} + 18 x - 2 = 0$
$D = {d}^{2} = {b}^{2} - 4 a c = 324 - 72 = 252 = 36 \left(7\right)$ --> $d = \pm 6 \sqrt{7}$
There are 2 real roots:
$x = - \frac{b}{2 a} \pm \frac{d}{2 a} = - \frac{18}{-} 18 \pm \frac{6 \sqrt{7}}{18} = 1 \pm \frac{\sqrt{7}}{3}$
$x = \frac{3 \pm \sqrt{7}}{3}$