As stated in the attached link, there are three possible discriminant conditions: Positive, Zero, or Negative. If the discriminant is negative, there are no real solutions but there are two imaginary solutions. So, yes there are solutions if the discriminant is negative. The solutions are imaginary, which is perfectly acceptable as solutions.
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If the discriminant is negaitve, there are no "real" solutions. The solutions are "imaginary".
It has two complex solutions.
2
6
imaginary