How do you solve #11x^2-x-3=0# using the quadratic formula?

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Answer 1 · 2015-08-10T07:35:46

The solutions for the equation are:
#color(blue)( x =(1+sqrt(133))/22#
#color(blue)( x =(1-sqrt(133))/22#

#11x^2−x−3 =0#

The equation is of the form #color(blue)(ax^2+bx+c=0# where:
#a=11, b=-1, c=-3#

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

# = (-1)^2-(4*11*(-3))#

#=133#

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

#x = (-(-1)+-sqrt(133))/(2*11) = (1+-sqrt(133))/22#

The solutions are:
#color(blue)( x =(1+sqrt(133))/22#
#color(blue)( x =(1-sqrt(133))/22#