Are you saying that you have developed two potential solutions but neither of them are valid when you check them?
There are four possibilities: 1. You made an error deriving the solutions that you have. 2. You made an error in checking the potential solutions. 3. There is another as yet undiscovered solution to the problem (If you are solving a quadratic and you found two potential solutions, then number 3 is NOT the problem). 4. The problem doesn't have a solution, which is to say that the solution set is the null set.
Check for situations 1, 2, and 3 very carefully before reporting the null set as the solution set.
John
My calculator said it, I believe it, that settles it