Find two consecutive positive integers such that thw sqaure of the first decreased by 25 equa; s three times the second

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