red = 4, green = 2, blue = 6 ⇒ total = 12
answer: discriminant is 36. there are two real solutions (both different)
the equation 1x^2 - 4x - 5 = 0 is in the form ax^2 + bx + c = 0. we see that
a = 1, b = -4, c = -5
so the discriminant is
d = b^2 - 4ac
d = (-4)^2 - 4()
d = 16 + 20
d = 36 is the discriminant
the discriminant is positive, so there are two different solutions. the solutions are both real.
note: because the discriminant is a perfect square, this means that the two solutions are rational (ie fractions of whole numbers).