찾았다 is a dictionary form of the verb. (past tense of 찾다) 찾았어 is more colloquial form of the verb. But you can use both in a daily life. When you found something and say "찾았다!", it is a monologue. But when you say "찾았어!", it is for telling your friend that you found it. (giving information) So you can ask a question like "찾았어?" "Have you found it?", but "찾았다?" doesn't make sense as a question.
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