Solve for x:
3 x^2+9 x-2 = 0
Divide both sides by 3:
x^2+3 x-2/3 = 0
Add 2/3 to both sides:
x^2+3 x = 2/3
Add 9/4 to both sides:
x^2+3 x+9/4 = 35/12
Write the left hand side as a square:
(x+3/2)^2 = 35/12
Take the square root of both sides:
x+3/2 = sqrt(35/3)/2 or x+3/2 = -sqrt(35/3)/2
Subtract 3/2 from both sides:
x = sqrt(35/3)/2-3/2 or x+3/2 = -sqrt(35/3)/2
Subtract 3/2 from both sides:
Answer: | x = sqrt(35/3)/2-3/2 or x = -3/2-sqrt(35/3)/2
