Given: #4x^2 = 6 + 5x#
To solve put the equation in the form: #Ax^2 + Bx + C = 0#
#4x^2 - 5x -6 = 0#
Factor:
Using the #AC#-method, #A*C = -24#.
You want two numbers that multiply to #-24# and sum to #B = -5#. Since #B# is negative, you want the larger number to be negative.
#" "ul(" "n_1 " "|" "n_2 " " |" "n_1 * n_2" "| " " n_1 + n_2" ")#
#" "-12" "2" "-24" "-10# doesn't work
#" "-8 " "3 " "-24" "-5# works
#C = -6#.
Since one of the numbers is #3#, the other number, #-8# must be divisible by #-2 = (-8)/-2 = 4# since #C = 3 * -2 = -6 #
#(4x + 3)(x - 2) = 0#
Set each term #= 0# to solve:
#4x + 3 = 0; " " x - 2 = 0#
#4x = -3; " " x = 2#
#4/4 x = -3/4#
#x = -3/4; " " x = 2#
