Review the item:
As her teachers had recommended, Madison tried to study in the
library but discovered that the good music,
unlimited soda, and big tables at the campus café made a great place
to do homework during fall semester, Madison must have eaten 150 pizza slices
while she slogged through Fundamentals of Biology.
No punctuation is necessary between library and but. Madison tried to study in the library but discovered ... is a main clause. This main clause has Madison as its subject and tried and discovered as its verbs.
Because there are only two verbs—two items in a series—a coordinating conjunction like but is enough to connect them.