To solve this equation, we first need to combine like terms on the left side:

8x^2 - 3x - 6x^2 + 1/12 = -1

Simplify:

2x^2 - 3x + 1/12 = -1

Next, move all terms to one side of the equation to set it equal to zero:

2x^2 - 3x + 1/12 + 1 = 0

2x^2 - 3x + 13/12 = 0

Now, we need to solve for x. We can use the quadratic formula to find the roots of this equation:

x = (-(-3) ± sqrt((-3)^2 - 42(13/12))) / (2*2)
x = (3 ± sqrt(9 - 104/12)) / 4
x = (3 ± sqrt(9 - 26/3)) / 4
x = (3 ± sqrt(27/3 - 26/3)) / 4
x = (3 ± sqrt(1/3)) / 4
x = (3 ± 1/sqrt(3)) / 4

So, the solutions for x are:

x = (3 + 1/sqrt(3)) / 4
x = (3 - 1/sqrt(3)) / 4