How do you solve #x² -3x-7=0#?

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Answer 1 · 2015-08-20T13:00:15

The solutions are
#color(blue)(x=(3+sqrt(37))/2#

#color(blue)(x=(3-sqrt(37))/2#

#x^2-3x-7=0#

The equation is of the form #color(blue)(ax^2+bx+c=0# where:
#a=1, b=-3, c=-7#

The Discriminant is given by:
#Delta=b^2-4*a*c#
# = (-3)^2-(4*1*-7)#
# = 9+28=37#

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

#x = (-(-3)+-sqrt(37))/(2*1) = (3+-sqrt(37))/2#

The solutions are
#color(blue)(x=(3+sqrt(37))/2#

#color(blue)(x=(3-sqrt(37))/2#