Two integers with the sum of -17 and the product of 52?

Let the integers be x and y
you have x+y=-17 (1)
xy=52 (2)
from eqn (1) x=-17-y (3)
, so subsitute eqn (3) in to eqn(2)
(-17-y)y=52
-17y-y²=52
:
-y²-17y-52=0 same as y²+17y+52=0
y²+13y+4y+52=0
y(y+13)+4(y+13)=0
(y+4)(y+13)=0
therefore y=-4 or -13
now substitute y=-4 or -13 in eqn (3)
x=-17-(-4) or -17-(-13)
x= -13 or -4
so when x=-13 ,y=-4 and when x=-4 ,y=-13

so the integers are -13 and -4