What two numbers multiply to get 54 and add to get 36?

Let the numbers be x and y.

given that their sum, x+y = 36

⇒ y = 36-x

product = xy = 54

⇒ x (36 - x) = 54

⇒ 36x - x² = 54

⇒ x² - 36x + 54 = 0

Solving the quadratic equation, we get

x = 18 + 3√30 and 18-3√30

So the numbers are 18 + 3√30 and 18-3√30