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

(x^2 - 1)/2 - (3x - 1)/4 = 2

Multiply each term by its respective denominator to get rid of the fractions:

2(x^2 - 1)/2 - 4(3x - 1)/4 = 2*2
x^2 - 1 - 3x + 1 = 4
x^2 - 3x = 4

Now we have a quadratic equation. To solve for x, we can set the equation equal to zero and factor or use the quadratic formula:

x^2 - 3x - 4 = 0
(x - 4)(x + 1) = 0

So, x = 4 or x = -1.

Therefore, the solutions to the equation are x = 4 or x = -1.