How do you solve # 3x^2 +6 =11x#?

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Answer 1 · 2016-05-04T17:36:39

The solutions are:

#x= 3 , x = 2/3#

#3x^2 + 6 = 11x#

#3x^2 - 11x + 6 =0 #

The equation is of the form #color(blue)(ax^2+bx+c=0# where:
#a=3, b=-11, c=6#

The Discriminant is given by:

#Delta=b^2-4*a*c#

# = (-11)^2-(4 * 3 * 6 )#

# = 121 - 72=49 #

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

#x = (-(-11)+-sqrt(49))/(2*3) = ((11+-7))/6#

#x = (11 +7) / 6 = 18/6 = 3#

#x = (11 -7) / 6 = 4/6 = 2/3#