complete the square

3x^{2} + 4x - 6 = 0 Given

(3x^{2} + 4x - 6)/3 = 0 Divide both sides by 3 (the coefficient of x^{2})

x^{2} + (4/3)x - 2 = 0 Divide each term by 3 (distributing)

x^{2} + (4/3)x = 2 Add 2 to each side

[(4/3)/2]^{2} = [2/3]^{2} = 4/9 Find the "(a/2b)^{2}" term

x^{2} + (4/3)x + 4/9 = 2 + 4/9 Add 4/9 to each side

(x + 2/3)^{2} = 2 + 4/9 Factor the left side into the perfect square

(x + 2/3)^{2} = 18/9 + 4/9 Find the common denominator for the right side

(x + 2/3)^{2} = 22/9 Simplify

x + 2/3 = +/- √(22/9) Take the square root of both sides

x + 2/3 = +/- √(22)/3 Simplify

x = -2/3 +/- √(22)/3 Subtract 2/3 from each side

x = (-2 +/- √(22))/3 Combine terms over the common denominator