Question

If -34=-34 how many solutions does it have ??

Answer 1

It is itself a solution, which makes 1 solution.
If, however, you had something like -34 + x = -34 + x, or -34x = -34x, as two examples, you might have infinite solutions, but unless a variable x, which is capable of holding infinite values, is included in your equality, then it must have a finite number of solutions.

Answer 2

It should only be 1? Unless I'm missing something here...

Hope that helps! :)