# How do you find the roots, real and imaginary, of y= -7x^2 -15x +(x-3)^2  using the quadratic formula?

Aug 17, 2017

see below

#### Explanation:

$- 7 {x}^{2} - 15 x + {\left(x - 3\right)}^{2} = 0$

$\implies - 6 {x}^{2} - 21 x + 9 = 0$

$\implies 6 {x}^{2} + 21 x - 9 = 0$

$a = 6 , b = 21 , c = - 9$
$x = \frac{- 21 \pm \sqrt{{\left(21\right)}^{2} - \left(4 \cdot 6 \cdot \left(- 9\right)\right)}}{2 \cdot 6} = \frac{- 7 \pm \sqrt{73}}{4}$