Learn English – With that or without “that”, which one is more formal to write

conjunctionsformalityoptional-that

I have this sentence:

There is an engine inside me that keeps saying "someone must be at the top, why isn't that you?"

Should I write that or leave it out?

I know both ways are correct, but I am asking for the most most most most most formal way.

You can't omit that when it's a subject, or your sentence becomes ungrammatical in standard English.

In this case, that is the subject of a that-relative clause:

There is an engine inside me
　　[ that keeps saying "someone must be at the top, why isn't that you?" ]_{that-relative clause}

In particular, it's the subject of the verb keeps. So you can't omit it, and there's no formal vs. informal distinction to be made.