The discriminant of a quadratic equation in the form ax^2 + bx + c = 0 is given by the formula D = b^2 - 4ac.
For the given quadratic equation 9w^2 + 54w + 81 = 0, we have a = 9, b = 54, and c = 81.
Calculating the discriminant:
D = (54)^2 - 4(9)(81)
D = 2916 - 2916
D = 0
Since the discriminant D is equal to 0, the quadratic equation has exactly one real solution.