Is the following situation possible?

Let their present ages be x and 20-x yrs respectively. Four years ago, their ages would be (x-4) and (16-x) yrs respectively.
(x-4)(16-x) = 48
16x - x² - 64 + 4x = 48
x² - 20x + 112 = 0
b² - 4ac = (-20)² - 4(1)(112) = 400 - 448 = -48
Since the discriminant < 0, the roots would be imaginary. Hence, such a situation is not possible.