Eight times the square of a positive integer divided by two equals 144 minus 36 times the positive integer. Find the unknown positive integer.

The correct answer for the question that is being presented above is this one: "The unknown positive integers are 3 and - 12."

Eight times the square of a positive integer divided by two equals 144 minus 36 times the positive integer.

8 * x^2 / 2 = 144 - 36x

4*x^2 = 144 - 36 x

x^2 = 36 - 9x

x^2 + 9x - 36 = 0

(x - 3) (x + 12) = 0

x - 3 = 0

x = 3

x + 12 = 0

x = - 12