To solve this equation, we will first distribute the coefficients on each term and then combine like terms.

1/4 x^2 + 1/4 2x - 1/4 7 - 1/3 x^2 - 1/3 x + 1/3 2 = 1/12 2x - 1/12 7 - 1/12 * x^2

Simplify each side:

1/4 * x^2 + 1/2x - 7/4 - 1/3x^2 - 1/3x + 2/3 = 1/6x - 7/12 - 1/12x^2

Combining like terms:

1/4x^2 - 1/3x^2 + 1/2x - 1/3x + 2/3 - 7/4 = 1/6x - 1/12x^2 - 7/12

(1/4 - 1/3)x^2 + (1/2 - 1/3)x + 2/3 - 7/4 = 1/6x - 1/12x^2 - 7/12

(3/12 - 4/12)x^2 + (6/12 - 4/12)x - 14/12 = 2/12x - 1/12x^2 - 7/12

-1/12x^2 + 2/12x - 14/12 = 2/12x - 1/12x^2 - 7/12

Combine like terms again:

-1/12x^2 + 2/12x - 14/12 = 2/12x - 1/12x^2 - 7/12

-1/12x^2 + 2/12x - 14/12 = 2/12x - 1/12x^2 - 7/12

Now, let's simplify:

-1/12x^2 + 2/12x - 14/12 = 2/12x - 1/12x^2 - 7/12

-1/12x^2 + 2/12x - 14/12 = 2/12x - 1/12x^2 - 7/12

-1/12x^2 - 2/12x + 2/12x + 1/12x^2 = -7/12 + 14/12

-1/12x^2 + 1/12x = 7/12

Now, we'll solve for x:

x(-1/12x + 1/12) = 7/12

x = (7/12) / (1/12) = 7

Therefore, the solution to the equation is x = 7.