Solution:
Quadratic equations are the polynomial equations of degree $2$ in one variable of type $f(x) = ax2 + bx + c$ where a, b, c, ∈ R and $a ≠ 0$.
Let the two integers be $x$ and $x+1$, $x$ taken as the smaller integer.
From the question, the product of these two integers is $306$
So,
$x(x + 1) = 306$
⇒$ x2 + x – 306 = 0$
Thus, the required quadratic equation is $ x2 + x – 306 = 0$