consecutive integers are 1 apart
so
square of the first decreased by 25 equals 3 time the 2nd
the 2 integers are x and x+1
x²-25=3(x+1)
distribute
x²-25=3x+3
minus (3x+3) from both sides
x²-3x-28=0
factor
what 2 numbers muliply to get -28 and add to get -3
-7 and 4
(x-7)(x+4)=0
set to zero
x-7=0
x=7
x+4=0
x=-4
false, we want positive integers
x=7
x+1=8
the inegers are 7 and 8