Car shakes above fifty mph even after tire balancing

This is typical of a front tire with a broken belt. That can be seen on the tire balancer, but only if the mechanic knows to look for it. The spinning tire is covered by a protective hood, so a broken belt cannot be seen without some additional effort.

This also depends on the service you asked for. If you requested a tire balance, based on what you read about other people's problems, that is what you got. If you asked to have a vibration solved, the repair would have started with a test-drive to verify the problem, then based on the mechanic's additional observations, he would have specifically inspected the tires for a broken belt and a bent wheel. If he found that, he would not have pursued the tire balance as he would know that would likely be a waste of money.

Tires needing to be re-balanced periodically is a fairly common service request that takes about a half hour. I do not know what makes you think we take your money and do no do anything to your car. It sounds like you consulted the internet for a common problem, but your car has a less-common problem that will not be solved with balancing the tires. If I am right, you should also see the steering wheel move back and forth when driving slowly through a parking lot, and if the broken belt is bad enough, you may feel the seat moving sideways too.

It is easier to see on the car, but you have to jack up at least one wheel so you can spin it. I run the car, in gear, on a hoist, but one wheel will always want to spin and the other one comes to a stop. That is normal. If you jack the car up so one tire is still on the ground, the other one will spin. If you jack it up so both tires are off the ground, inspect the tire that spins, then apply the brakes to stop it, shift to neutral if necessary, then put a block of wood under that tire. That will force the other tire to spin when you put it in "drive" again.

The easiest broken belt to spot looks like a tumor, or hump, on one side of the tread, and in just one part of the tire. Those are easy to see as the tire spins, but not always easy to see when just looking at a stationary tire. When a belt is really badly broken, the entire tread will squirm left and right as it rotates. Those are the ones that can make you seasick just driving slowly down the road.

The hardest broken belts to find are usually overlooked by most untrained mechanics. The belt comes apart so slowly that as the hump in the tread forms, it wears down from normal driving. That makes the tread appear to be perfectly fine. What you have to look for is the tread at the bottom of the grooves. One or two of those grooves might be rising and falling as the tire rotates, but the part of the tread that contacts the road surface looks okay.

The best place to go for this is a tire and alignment specialty shop. I learned how to spot those more elusive broken belts from a service adviser/salesman at a mass merchandiser, in the mid 1980's. I was taking old tires home to use on my cars, and they would always develop the vibrations after a few weeks. I could see the broken belts then, but it stumped me how he knew they were causing problems when they looked fine otherwise. He was looking at the grooves in the tread, not just the tread surface. That is what the specialists at the tire and alignment shops look for too.