subtract 12x from both sides and add 9 to both sides to get:
4x^2 - 12x + 9 = 0
the quadratic is now in standard form.
a = 4
b = -12
c = 9
quadratic formuls is x = (-b + sqrt(b^2-4ac)/(2a) or x = (-b-sqrt(b^2-4ac)/(2a)
-b is equal to 12
b^2 - 4ac is equal to 144-4*4*9 = 144 - 144 = 0
2a is equal to 8
formula becomes x = (12 + 0)/8 or x = (12-0)/8
this results in x = 12/8 or 12/8 which results in x = 3/2 or 3/2 which results in x = 3/2.
this could also have been factored using the split the middle term technique.
start with 4x^2 - 12x + 9 = 0
multiply 4 * 9 = 36
look for the factors of 36 that add up to -12
you will see that those factors are 6 * 6 = 36 and -6 - 6 = 12
split the middle term to get 4x^2 - 6x - 6x + 9 = 0
group the first 2 terms and the last 2 terms to get:
(4x^2 - 6x) - (6x - 9) = 0
factor 2x from the first grouping and factor 3 from the second grouping to get:
2x * (2x - 3) - 3 * (2x - 3) = 0
factor out the (2x - 3) to get:
(2x - 3) * (2x - 3) = 0
solve for x to get x = 3/2 or x = 3/2
this results in x = 3/2.
the graph of your equations looks like this.
you will see that the equation = 0 when x = 3/2 which becomes x = 1.5.
