# How do you find the roots, real and imaginary, of y=-23x^2+5x+2 using the quadratic formula?

##### 1 Answer
May 20, 2016

$\frac{5 \pm \sqrt{209}}{46}$

#### Explanation:

Use the improved quadratic formula (Socratic Search)
$y = - 23 {x}^{2} + 5 x + 2 = 0$
$D = {d}^{2} = {b}^{2} - 4 a c = 25 + 184 = 209$ --> $d = \pm \sqrt{209}$
There are 2 real roots:
$x = - \frac{b}{2 a} \pm \frac{d}{2 a} = - \frac{5}{-} 46 \pm \frac{\sqrt{209}}{-} 46 =$
$= \frac{5 \pm \sqrt{209}}{46}$