The product of two consecutive positive integers is 306.

Since it is given in the question that the numbers we have to find are consecutive positive integer numbers, therefore the difference between the two numbers should be equal to 1.
For e.g. 7 and 8 or 26 and 27 are consecutive numbers.

Let us assume the first number to be ‘x’. So our next consecutive number should be ‘x + 1’. Now the question also says that the product of these two numbers is 306.

Therefore,

$(x)(x+1)=306$

$x^{2}+x=306$

$x^{2}+x-306=0$

Hence, this is our required quadratic equation.