x2-2x-13=0

I need square root on both sides.

Hmmmm. OK

sqrt(x^2-2x-13)=0

I am really wondering what you are trying to do. If you are solving it by completing the square, then

x^2-2x=13
x^2-2x+1=14
(x-1)^2= 14
x-4=+-sqrt14
x= 4+-sqrt14