First, let's simplify the left side of the equation by dividing each term by 2:

(2x^2 + 3x - 35)/2 = x^2 + 6x - 12
x^2 + (3/2)x - 35/2 = x^2 + 6x - 12

Now, let's combine like terms and set the equation equal to zero:

(3/2)x - 35/2 = 6x - 12
(3/2)x - 6x = 35/2 - 12
(-9/2)x = 35/2 - 24/2
(-9/2)x = 11/2

Now, let's solve for x by multiplying both sides by -2/9:

x = 11/2 * -2/9
x = -22/18
x = -11/9

Therefore, the solution is x = -11/9.