You actually "solved" numerator (whatever that means - a better term would be "factor"). The denominator is always positive; just complete the square to show this. I would agree with your region in general. Are the endpoints included, do you think?
What values of x make y real.
I solved the denominator and got x=2, -7. So I figured that if x is between -7 and 2 the denominator will be a real value.
http://i53.tinypic.com/2q2470j.jpg