Question 27767
Let the consecutive integers be x, and x+1


{{{(x)^2+(x+1)^2=85}}}
{{{x^2+(x^2+1+2x)=85}}}
{{{2x^2+1+2x=85}}}
{{{2x^2+2x-84}}}
{{{x^2+x-42}}}


Factor: 
(x+7) and (x-6)


Remove the negative left with x= 6
6+1=7


Hence, the two integers are 6 and 7.
Paul.