Final answer:
The equation of the sphere is (x - 5)^2 + (y + 4)^2 + (z - 2)^2 = 9^2.
Step-by-step explanation:
The equation of a sphere can be represented as (x - h)^2 + (y - k)^2 + (z - l)^2 = r^2, where (h,k,l) represents the center of the sphere and r represents the radius.
In this case, the center of the sphere is (5, -4, 2) and the radius is 9. Plugging these values into the equation, we get the equation of the sphere as (x - 5)^2 + (y + 4)^2 + (z - 2)^2 = 9^2.