If the discriminant, given by b^2 - 4ac, is equal to zero, it means that there is only one real solution to the quadratic equation ax^2 + bx + c = 0.
When the discriminant is zero, it indicates that the quadratic equation has a perfect square trinomial as its factor, resulting in the quadratic equation having repeated roots.
Therefore, in the given scenario where b^2 - 4ac = 0, the number of real solutions of the equation ax^2 + bx + c = 0 is one.