Question 246073
let x=first integer and y= second integer
x=2y+5
xy=52
substitute 2y+5 for x in the second equation

(2y+5)*y=52
2y^2+5y=52
divide by 2
y^2+5/2=26
we will complete the square
take (5/2)/2 and square it
(5/4)^2=25/16
convert 26 to improper fraction with 16 as the denominator
y^2+5/2=416/16
add 25/16 to both sides
y^2+5/2+25/16=416/16+25/16
y^2+5/2+25/16=441/16
factor left hand side
(y+5/4)^2=441/16

|y+5/4|=21/4
y+5/4=-21/4
y+5/4=21/4
subtract 5/4 from both sides
y=-26/4=-13/2
y=16/4=4
 only 4 is a positive integer
4*x=52
x=13
so the two integers are 4 and 13
check 
2(4)+5=8+5=13 
ok