solve for x: by completing the square:
(3 x^2 - 4 x + 2)/(3 x - 19) = 0
Multiply both sides by 3 x - 19:
3 x^2 - 4 x + 2 = 0
Divide both sides by 3:
x^2 - (4 x)/3 + 2/3 = 0
Subtract 2/3 from both sides:
x^2 - (4 x)/3 = -2/3
Add 4/9 to both sides:
x^2 - (4 x)/3 + 4/9 = -2/9
Write the left hand side as a square:
(x - 2/3)^2 = -2/9
Take the square root of both sides:
x - 2/3 = (i sqrt(2))/3 or x - 2/3 = -(i sqrt(2))/3
Add 2/3 to both sides:
x = 2/3 + (i sqrt(2))/3 or x - 2/3 = -(i sqrt(2))/3
Add 2/3 to both sides:
Answer: x = 2/3 + (i sqrt(2))/3 or x = 2/3 - (i sqrt(2))/3
