# How do you solve -5x^2 + 5x + 60 = 0 using the quadratic formula?

Aug 12, 2015

#### Answer:

The solutions are
color(blue)(x=-3, x=4

#### Explanation:

−5x^2+5x+60=0

The equation is of the form color(blue)(ax^2+bx+c=0 where:
$a = - 5 , b = 5 , c = 60$

The Discriminant is given by:

color(blue)(Delta=b^2-4*a*c

$= {\left(5\right)}^{2} - \left(4 \cdot \left(- 5\right) \cdot 60\right)$

$= 25 + 1200 = 1225$

The solutions are found using the formula:

color(blue)(x=(-b+-sqrtDelta)/(2*a)

$x = \frac{\left(- 5\right) \pm \sqrt{1225}}{2 \cdot \left(- 5\right)} = \frac{\left(- 5 \pm 35\right)}{-} 10$

Solution 1:

$x = \frac{- 5 + 35}{-} 10 = \frac{30}{- 10}$

color(blue)(x=-3

Solution 2:

$x = \frac{- 5 - 35}{-} 10 = - \frac{40}{-} 10$

color(blue)(x=4