20 lbs. in 7 weeks is not impossible but it would be very difficult. Particularly if you are just 30 lbs. overweight. You would be losing around 2.86 lbs./week which would require a 10,000 calorie/week deficit. This all comes out to around a 1429 calories/day deficit.
You definitely should not try this with just a diet and should still take in at least 1400-1600 calories/day. I would recommend lots of cardio (30+ minutes, 4-6 days/week) but you should probably re-examine your goal and try to lose between 1 and 2 pounds per week.
I hope this helps
