Three times the square of a certain positive number exceeds six times the number by nine Find the number?

The problem can be written as

3x2 = 6x + 9

x is the number we want to find

Solution:

x2 = 2x + 3

x2 - 2x - 3 = 0

(x-3)(x+1) = 0

x = -1, 3