2001 Jeep Cherokee car shakes at 50 mph

Have the front end inspected for bad bushings or rod ends. Also have them check the tires, if anyone has used a liquid tire sealer, it can cause strange vibrations at those speeds from it moving around in the tire. Doubt it is brake issue, then the wheel would saw back and forth when you applied the brakes. Beware of chain stores, they live off the up-sell and could replace the entire front end for a smaller problem. Ask around for referrals for a brake/front end shop that friends/family uses.