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A mathematician would say that each (a,b,c) produces one x, a complex
number. S/he would be interested in distributions or the real and
imaginary parts of x, as clarified yesterday.
A physicist or engineer, on the other hand, dealing with a specific
case, would have to decide whether or not the imaginary (or
negative-real) solutions make sense. Suppose the x stands for the mass
of an object. In that case negative solutions would be ignored.