How do you solve #5x^2+9x-2=0# using the quadratic formula?

1 Answer
Jul 25, 2015

Answer:

The solutions for the equation are:
#color(blue)(x=-2,x=1/5#

Explanation:

The equation #5x^2+9x−2# is of the form #color(blue)(ax^2+bx+c=0# where:
#a=5, b=9, c=-2#

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

#= (9)^2 - (4)* (5) * (-2)#

#= 81+40 = 121#

As #Delta>0# there are two solutions.

The solutions are found using the formula
#x=(-b+-sqrtDelta)/(2*a)#

As #Delta =121#, #x = ((-9)+-sqrt(121))/(2*5) = (-9+-11)/10#

#x=((-9-11)/10) = -20/10 =color(blue)( -2#

#x=((-9+11)/10) = 2/10 =color(blue)( 1/5#