How do you solve #3x^2+8=12x# by using the Quadratic Formula?

1 Answer
Jul 21, 2015

Answer:

#x = 2 +- 4/sqrt(3)#
#color(white)("XXXX")##color(white)("XXXX")#(solved using the Quadratic Formula)

Explanation:

Using the standard quadratic form:
#color(white)("XXXX")##ax^2+bx+c=0#
the quadratic formula for the solutions is
#color(white)("XXXX")##x = (-b+-sqrt(b^2-4ac))/(2a)#

It will be necessary, first to convert the given equation:
#color(white)("XXXX")##3x^2+8=12x#
into the standard form (by subtracting #(12x)# from both sides):
#color(white)("XXXX")##3x^2-12x+8 = 0#

Therefore, using:
#color(white)("XXXX")##a= 3##color(white)("XXXX")##b=-12##color(white)("XXXX")##c=8#

The quadratic formula gives
#color(white)("XXXX")##x = (12 +-sqrt((-12)^2 - 4(3)(8)))/(2(3))#

#color(white)("XXXX")##x = (12 +-sqrt(144 -96))/6#

#color(white)("XXXX")##x = 2 +- 4/sqrt(3)#