It is grammatically fine.

Idiomatically, it is now old-fashioned. as Edwin Ashworth said; but it used to be quite common to use the negative where we would use the positive in offering things:

Won't you come this way?

 

Wouldn't you like to sit down?

and trying things:

Let's see if we can't fix this.

It is grammatically fine.

Idiomatically, it is now old-fashioned. as Edwin Ashworth said; but it used to be quite common to use the negative where we would use the positive in offering things:

Won't you come this way?

Wouldn't you like to sit down?

and trying things:

Let's see if we can't fix this.