Question

x^-2 -x^-1 -1=0

Answer 1

1/x^2 - 1/x - 1 = 0

Answer 2

Find the common denominator, which is x^2, and multiply everything by it. You'll end up with:
1 - x - x^2 = 0

Answer 3

Or, if you multiply everything by -1 and rearrange..
x^2+x-1=0

Answer 4

I don't think that's factorable, so just use the discriminant formula:
D = b^2-4*a*c, where b=1, a=1, c=-1

Answer 5

D = 1 - 4*1*(-1) = 1+4=5

Answer 6

x1 = (-b-sqrt(D))/(2a)
x2 = (-b+sqrt(D))/(2a)

x1 = (-1-sqrt(5))/2
x2 = (-1+sqrt(5))/2