How do you solve #3x (x - 2) = 1#?

1 Answer
Aug 19, 2015

Answer:

The solutions are
#color(blue)(x=(3+2sqrt3)/3#
#color(blue)(x=(3-2sqrt3)/3#

Explanation:

#3x(x−2)=1#

#3x^2−6x=1#

#3x^2−6x-1=0#

The equation is of the form #color(blue)(ax^2+bx+c=0# where:
#a=3, b=-6, c=-1#

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

# = (-6)^2-(4*3*(-1))#

# = 36+12=48#

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

#x = (-(-6)+-sqrt(48))/(2*3) = (6+-4sqrt(3))/6#

#( cancel2(3+-2sqrt(3)))/cancel6 = (3+-2sqrt3)/3 #

The solutions are
#color(blue)(x=(3+2sqrt3)/3#
#color(blue)(x=(3-2sqrt3)/3#