Solve for x over the real numbers using the quadratic formula.
9 x^2 - 12 x + 4 = 4
Subtract 4 from both sides:
9 x^2 - 12 x = 0
9 x^2 - 12 x = 3 (3 x^2 - 4 x):
3 (3 x^2 - 4 x) = 0
Divide both sides by 3:
3 x^2 - 4 x = 0
x = (4 ± sqrt((-4)^2 - 4×3×0))/(2×3) = (4 ± sqrt(16 + 0))/6 = (4 ± sqrt(16))/6 = (4 ± 4)/6:
x = (4 + 4)/6 or x = (4 - 4)/6
(4 + 4)/6 = 8/6 = 4/3:
x = 4/3 or x = (4 - 4)/6
(4 - 4)/6 = 0/6 = 0:
Answer: x = 4/3 or x = 0
