I'm thinking of a number. My number has the property that its square is equal to $270$ more than five times the number. Enter all numbers that have this property.

Let your number be x, a variable. x has the property that x^2 = 5x + 270; x^2 - 5x - 270 = 0

By quadratic formula, \(x = {5\pm5\sqrt{55}\over2}\), which are your two numbers that you may be thinking of.