This pattern is common in spoken Japanese for seeking agreement or confirming something you believe to be true. When used with a falling intonation, it means 'right?' or 'isn't it?'. For example, if you see a friend looking tired, you might say '疲れたじゃないか' meaning 'You're tired, aren't you?' It can also be used to express surprise or realization, like 'あ、ここにあったじゃないか' meaning 'Oh, it was here after all.'

When used with a rising intonation and with a suggestion to do something, it often functions like 'let's' or 'why don't we?' For instance, 'そろそろ行くじゃないか' means 'Why don't we go soon?' This usage is more assertive than a plain suggestion, but still friendly.

In casual speech, 'じゃないか' often becomes 'じゃない' (dropping the か) with a rising tone. However, that is a separate casual form; the basic pattern with か is fine in everyday conversation and is not too formal.