Is it possible to lose 45 pounds in 21 weeks in a healthy way?

Yes. It is possible to lose a rapid amount of weight in a short period of time (most notably with medical problems such as cancer, hiv), but for someone interested in losing weight for health/fitness reasons, it is certainly not recommended. To lose weight and maintain weight loss, it is recommend that you lose no more than 1-2 lbs (0.5-1 kg)/week.