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

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Answer 1 · 2015-08-12T06:03:46

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

#−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#

# = (5)^2-(4*(-5)*60)#

# = 25 + 1200=1225#

The solutions are found using the formula:

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

#x = ((-5)+-sqrt(1225))/(2*(-5)) = ((-5+-35))/-10#

Solution 1:

#x=(-5+35)/-10 = 30/(-10)#

#color(blue)(x=-3#

Solution 2:

#x=(-5-35)/-10 = -40/-10#

#color(blue)(x=4#