How do you solve #3x^2 + 4 = -7x# using the quadratic formula?

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Answer 1 · 2015-08-11T17:19:32

The solutions are
#color(blue)(x=-4/3 ,x=-1#

#3x^2+4=−7x #

#3x^2+ 7x+4=0 #

The equation is of the form #color(blue)(ax^2+bx+c=0# where:
#a=3, b=7, c=4#

The Discriminant is given by:
#Delta=b^2-4*a*c#
# = (7)^2-(4*3*4)#
#=49-48#
# = 1#

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

#x = ((-7)+-sqrt(1))/(2*3) = (-7+-(1))/6#

#x=(-7-1)/6=-8/6 = -4/3#

#x=(-7+1)/6=-6/6 = -1#

The solutions are
#color(blue)(x=-4/3 ,x=-1#