To solve this quadratic equation, we first want to see if it can be factored.

Given equation: 12у^2 - у - 6 / 3у^2 + 5у + 2 = 0

We can simplify the expression:

(3у + 2)(4у - 3) / (3у + 2)(у + 1) = 0

Now we can cancel out the common factors:

4у - 3 / у + 1 = 0

Now, we have a linear equation that can be easily solved by setting the numerator equal to zero:

4у - 3 = 0
4у = 3
у = 3/4

Therefore, the solution to the equation 12у^2 - у - 6 / 3у^2 + 5у + 2 = 0 is у = 3/4.