We can represent the integers with x and x + 2. The reason why the second number is x+2 is that odd numbers are 2 integers away from each other.
x(x+2) = 783
x^2 + 2x - 783 = 0
(x - 27)(x + 29)=0
The consecutive odd integers could either be 27 and 29, or -29 and -27
