Note
The たら form is ungrammatical here, because the library is quiet is not something that happens after you're going to study.
Breakdown of benkyousuru nara, toshokan ga shizuka desu. benkyoushitara, toshokan ga shizuka desu.
ですdesu
to be
がga
subject particle
勉強するbenkyousuru
to study
図書館toshokan
library
静かshizuka
quiet
。。。 なら... nara
if ... is the case
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