How do you solve #x^2+5x-84=0# using the quadratic formula?

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Answer 1 · 2015-08-10T07:48:06

The solutions for the equation are:
# color(blue)(x=7# , # color(blue)(x=-12#

#x^2+5x−84=0 #

The equation is of the form #color(blue)(ax^2+bx+c=0# where:
#a=1, b=5, c=-84#

The Discriminant is given by:
#Delta=b^2-4*a*c#

# = (5)^2-(4*1*(-84))#

# = 25 + 336 = 361#

The solutions are found using the formula:

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

#x = ((-5)+-sqrt(361))/(2*1) = ((-5+-19))/2#

The solutions are:
#x= ((-5+19))/2 = 14/2 , color(blue)(x=7#

#x= ((-5-19))/2 =-24/2, color(blue)(x=-12#