Question 789858
let the integers be x & x+2

1/x + 1/(x+2) =9/40

multiply equation by 40x(x+2)

40(x+2)+40x=9x(x+2)

40x+80+40x=9x^2+18x

9x^2+18x-80x-80=0

9x^2-62x-80=0

solve by quadratic formula

a=	9	,	b=	-62	,	c=	-80
							
b^2-4ac=	3844	+	2880				
b^2-4ac=	6724						
{{{	sqrt(	6724	)=	82	}}}		
{{{x=(-b+-sqrt(b^2-4ac))/(2a)}}}							
{{{x1=(-b+sqrt(b^2-4ac))/(2a)}}}							
x1=(	62	+	82	)/	18		
x1=	8.00						
{{{x2=(-b-sqrt(b^2-4ac))/(2a)}}}							
x2=(	62	-82	) /	18			
x2=	-1.11						

8 is an integer

so the integers are 8 & 10