wyjść z tarapatów in inglese:

There was some doctor here and he said that Jack's life was out of the woods.

It's too soon to say if either airline is out of the woods yet.

I think we’re out of the woods now

It's still too soon to say they are out of the woods. We had some financial difficulties but we are finally out of the woods. Once you come up with the title for your thesis and an outlet, you will be out of the woods

(he left hospital so now he's officially out of the woods)