Chest xrays are wonderful and they can show many things. They can save lives and alert of problems too. They are very helpful in ruling out certain conditions of the lungs and chest so that more time can be spent looking in other areas. They cannot, however, actually discover an embolism in most cases. But, they can be helpful all the same. An xray is often taken when a clot is suspected even though it can't show one.
Blood clots do not show up on xrays is the reason that xrays don't discover them. But, xrays show many things that can point to the problem being caused by an embolism. There are other tests that can show one and tests that are useful in diagnosing chest and lung problems that migh cause an embolism. All tests can be combined to ultimately find out if an embolism is present...or not.