。
She was eager to know the entrance exam results.
Literal
She [topic-は] entrance-exam's results [object-を] [eagerly-しきりに] [was-wanting-to-know-知りたがっていた].
しきりに ('eagerly, repeatedly, persistently') is a 擬態語-flavored adverb conveying urgent recurrence. 知りたがる combines 知る ('know') + ~たい ('want to') + ~がる (third-person observable desire) — and the whole is in past progressive ~ていた.