The general rule is to not use contractions such as "isn't" for formal writing, such as academic papers and business proposals.
For speaking, it's natural to use contractions. During rapid speech, people will contract words that are not even formally recognized as contractions or taught in English classes.
While speaking however, when you want to emphasize the negative "not" or to be very clear, you will use the long form. For example, when you are arguing about something with your friend, "No, he's NOT. He's NOT married." Notice that I even contracted "he is not" as "he's not" and not "he isn't," because I'm emphasizing the negative.