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We need to select two consecutive i.e. values which come after each other.

Therefore,

Let the two consecutive positive integers be x and(x+1),

Here we take x as the first integer and so the next number coming after it is (x+1)

For example, 2 comes after 1 and 2=1+1

Then according to the problem,

Their product is;

x(x+1)=240

On multiplying the two variables on the left hand side we get,

$x^{2}-x-240=0$

This is the required quadratic equation. Thus, when two consecutive positive integers are multiplied we get the equation we got above.