You can tell by looking at the problem that it will be quadratic, as the highest exponent x will have is two, but if you want to work it out follow these steps:
Original Equation (x + 3)(x - 4) = 8
Distribute x^2+3x-4x-12=8
Combine like terms. x^2-x-12=8
Subtract 8 from both sides x^2-x-20=0 or y
Your final equation is y=x^2-x-20, and you can see that the highest exponent for the x is 2, so the equation is quadratic.