How do i do this ? this is a very difficult problem

With that table of values, you can come up with a slope intersect form of a line
7 = -8m + b
1 = -5m + b
-5 = -2m + b

7-1 = -3m
6 = -3m
m  = -2
1 = -5 * -2 + b
b = 1 - 10
b = -9
so it is    y = -2x - 9

Now we can find where those intersect 

-2x - 9 =2 (x+4)^2 - 5
-2x - 9 = 2(x^2 + 8x + 16) - 5
-2x - 9 = 2x^2 +16x + 32 -5
2x^2 + 18x +36 = 0
x^2 + 9x + 18 = 0

D = 81 - 72 = 9 = 3^2
x1 = (-9 - 3) / 2 = -6;   y1  = 3
x2 = (-9 + 3) / 2 = -3; y2 = -3

so the solutions are (-6; 3) and (-3; -3)