Two positive numbers have a difference of 4 and a product of 96. what are the numbers?

Hello :
the numbers are : x , y 
x - y = 4...1)
xy = 96...(2)
by (1) : x = y +4...(*)
subsct in (2) : (y+4) y = 96
y² +4y -96 = 0
(y² +2(2y) +2²) -2² -96 = 0
(y+2)² -100 =0
 (y+2)² = 10²
y +2 = 10 or y+2 = -10
y = 8 or y = -12 ( refused : x is positif)
y = 8
subsct in (*) : x = 8+4 = 12
 the numbers are : 12 and 8 
12-8 = 4   and 12×8 = 96