The square of a natural number is 24 more than 5 times the number. What is the number?

Suppose the number is x. Then x2 = 5x + 24

or x2 - 5x - 24 = 0

Then x2 - 8x + 3x - 24 = 0 or x(x - 8) + 3(x - 8) = 0

that is (x - 8)*(x + 3) = 0

so that x = 8 or x = -3

Since the number is a natural number, it cannot be -3, and so the answer is 8.