Welcome to the forum. If you are handy with tools, you can adjust the cam chain yourself. We have the factory service manuals available for free download. Go to the home page of our forum, look for the Manuals posting (it should be pinned for easy access), and find the DOHC manual. In there, you'll learn how to do all sorts of maintenance on your bike.
I would worry more about the cam chain than the carbs at first. A broken cam chain can lead to a very expensive rebuild of the motor. It's easy enough to adjust: takes about 5-10 minutes, assuming all the fasteners come loose like they're supposed to. While you're waiting, go to the home page, type in cam chain adjustment in the search window, and read the post results.
You can ride the bike without the carbs being in sync. Sync-ing the carbs makes sure every cylinder is operating equally (pulling its own weight, so to speak). Your bike will run smoother and quieter. The process is a bit involved and requires some special equipment. If your shop has the gauges and screwdrivers, it may be cheaper to have them do it.
Good luck, and keep us in the loop. Ride safe.
Luke M
Used to have a 1979 CB750L, sold it as a parts bike, now riding a slightly modified 1984 VT700C. Network/Field Engineer. Central OH, USA, Earth, Sol System, Milky Way Galaxy, Universe.