How do you solve #x^2 - 3x = -6x - 1#?

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Answer 1 · 2015-08-02T06:39:28

The solutions for the expression are
#color(green)(x=(-3-sqrt5)/2, x=(-3+sqrt5)/2#

#x^2−3x=−6x−1#

#x^2−3x+6x+1=0#

#x^2+3x+1=0#

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

The Discriminant is given by:
#Delta=b^2-4*a*c#
# = (3)^2-(4*(1)*1)#
# = 9-4=5#

As #Delta>0# there are two solutions.

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

#x = ((-3)+-sqrt(5))/(2*1) = (-3+-sqrt(5))/2#

The solutions for the expression are:
#color(green)(x=(-3-sqrt5)/2, x=(-3+sqrt5)/2#