Comment by Tainnor

It's true that it might be unexpected that there is no real solution. I also wouldn't have intuited that from the problem statement itself.

However, it's not like you have to go out of your way to look for the complex numbers in some creative way. At some point while solving the quadratic equation you'll have to take the root of a negative number. So the only choice is to reach for the complex numbers, your hand is kinda forced.