Question 421708
Solution: Denote x the first integer and x+1 the consecutive integer.
          Their sum is x+(x+1)=2x+1, while their product is {{{x(x+1)= x^2+x}}}
Base on the given data, we write the equation; {{{(x^2+x)-(2x+1)=19}}}. We solve this quadratic equation.

      {{{ x^2+x-2x-1-19=0 }}}

      {{{ x^2-x-20=0 }}}

      {{{ (x-5)(x+4)=0 }}}

        {5, -4} are the roots of our equation. 

Answer: Our problem have two solutions: The integers that satisfy the problem are:
       a) 5 and 6, because 5X6-(5+6)=19.
       b) -4 and -3, because, (-4)x(-3)-(-4-3)=12+7=19.