This just happens all the time. For example, to get the free-fall time for a falling object, you have to take a quadratic root of an expression, which in principle gives a "negative time" root/solution. This solution is obviously nonsense, so you just discard it and don't pay attention to it, but you don't conclude that the theory is wrong.

If you don't discard it, and do pay attention to it, you discover it is sensible.

"Negative time" is time before the time you labelled as zero. The negative solution is the time at which the object would have been at the end point, moving upwards, to get to the starting point at time zero.