Help with what?
You have given us two different circles.
What do you want to do?
They do intersect. Here is a picture of your problem
http://www.wolframalpha.com/input/?i=plot+x%5E2%2By%5E2%2B6y%2B5%3D0+,+x%5E2%2By%5E2-2x-8%3D0
Please help!!
x^2+y^2+6y+5=0
x^2+y^2-2x-8=0
2 answers
you want
x^2+y^2+6y+5 = x^2+y^2-2x-8
6y+5 = -2x-8
y = -(2x+13)/6
Now use that to find x:
x^2 + (-(2x+13)/6)^2 - 2x - 8 = 0
40x^2 - 20x - 119 = 0
x = [5±9?15]/20
y = -3/20 (15±?15)
http://www.wolframalpha.com/input/?i=solve+x%5E2%2By%5E2%2B6y%2B5%3D0,+x%5E2%2By%5E2-2x-8%3D0
x^2+y^2+6y+5 = x^2+y^2-2x-8
6y+5 = -2x-8
y = -(2x+13)/6
Now use that to find x:
x^2 + (-(2x+13)/6)^2 - 2x - 8 = 0
40x^2 - 20x - 119 = 0
x = [5±9?15]/20
y = -3/20 (15±?15)
http://www.wolframalpha.com/input/?i=solve+x%5E2%2By%5E2%2B6y%2B5%3D0,+x%5E2%2By%5E2-2x-8%3D0