In general, cholesterol stones smaller than 15 mm (about 80% of gallstones are cholesterol stones) can be dissolved with bile acids. If an ultrasound scan shows a gallstone but it is not visible on X-ray, it is a cholesterol stone.
Please read the following article:
How can gallbladder polyps and gallstones be treated with bile acids?
If the X-ray also shows gallstones, they are definitely calcareous, hard stones, and it is not possible to dissolve them at the moment.
Please read the following article:
Curing gallstones with gallstone crushing