Completing the square

First, re-arrange and divide through by 3 to get

x^2 +7/3x = 2        take 1/2 of the 'x' co-efficient and square it and add it to both sides

x^2 + 7/3x + 49/36  = 2 + 49/36

Simplify to:

(x+7/6)^2  =3 13/36        Take the square root of both sides

x+7/6  =  +- sqrt (3 13/36)   Calculator to get

x + 7/6   = +-  1.83333           Subtract 7/6 from both sides

x = -7/6 + 1.83333   or  - 7/6 - 1.83333     Simplify

x  = .66666       or   -2.99999           

or x = 2/3   or  -3    (rounded)             Then substitute the answers into the equation to see if true  (they are)

Solve for x:
3 x^2 + 7 x - 6 = 0

Divide both sides by 3:
x^2 + (7 x)/3 - 2 = 0

Add 2 to both sides:
x^2 + (7 x)/3 = 2

Add 49/36 to both sides:
x^2 + (7 x)/3 + 49/36 = 121/36

Write the left hand side as a square:
(x + 7/6)^2 = 121/36

Take the square root of both sides:
x + 7/6 = 11/6 or x + 7/6 = -11/6

Subtract 7/6 from both sides:
x = 2/3 or x + 7/6 = -11/6

Subtract 7/6 from both sides:
Answer: |x = 2/3        or        x = -3