Find two consecutive positive integers such that the square of the smaller increased by 4 times the larger is 64.

Answer 1

let the two numbers be x and x+1
x^2 + 4(x+1) = 64

x^2 + 4x + 4 - 64=0
x^2 + 4x - 60 = 0
(x+10)(x-6) = 0
x = -10 or x = 6
but you wanted only positive integers, so x = 6

the two numbers are 6 and 7

check:
What is 6^2 + 4(7) ??