# How do you find the roots, real and imaginary, of y=-5(x-2)^2+3x^2-15  using the quadratic formula?

Jun 9, 2018

color(violet)(x = 5 + sqrt 15, 5 - sqrt15

#### Explanation:

$y = - 5 {\left(x - 2\right)}^{2} + 3 {x}^{2} - 15$

$y = - 5 {x}^{2} + 20 x - 20 + 3 {x}^{2} - 15$

$y = - 2 {x}^{2} + 20 x - 35$

$x = \frac{- 20 \pm \sqrt{{20}^{2} - 280}}{-} 4$

$x = \frac{- 20 \pm \sqrt{120}}{-} 4$

color(violet)(x = 5 + sqrt 15, 5 - sqrt15