Nine times a whole number is equal to five less than twice the square of the number. Find the number?

Question: Nine times a whole number is equal to five less than twice the square of the number. Find the number?

Solution:
Let the required whole number be x.

According to the question,
9x = 2x² - 5
⇒ 2x² - 9x - 5 = 0
⇒(x - 5)(2x + 1) = 0
⇒ x - 5 = 0 or 2x + 1 = 0
⇒ x = 5 or x = - 1/2

Since x is supposed to be a whole number, the answer, i.e., the required whole number is 5.