The midpoint of AB is M(2,-2). If the coordinates of A are (8,1), what are the coordinates of B?
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The discriminant is the bit under the radical, the .
Because it's under a radical, it's what tells you how many and what kind of solutions you have (two real, one real, or two imaginary/complex solutions).
Does that answer your question? Or do you need an example?
Suppose you had the equation , then you'd have:
,
and
You'd plug those values into to see if the discriminant was positive, zero, or negative:
Since that is 37 (a postiive number), you'd have two real solutions.