Represent the following problem situations in the form of quadratic equations:
The product of two consecutive positive integers is 306. We need to find the integers.

Let two consecutive positive integers are x and (x + 1). Then
x(x + 1) = 306
⇒ x² + x – 306 = 0
which is a quadratic equation in x.
Solving this equation by factorisation method, we get
x² + 18x – 17x – 306 = 0
⇒ x(x + 18) – 17(x + 18) = 0
⇒ (x + 18) (x – 17) = 0
⇒ x + 18 = 0 or x – 17 = 0
⇒ x = –18 or x = 17
But integers are +ve
∴ x = 17
Hence, two consecutive positive integers are 17 and 18.