0=y^2-2y-1

Solution for 0=y^2-2y-1 equation:

0=y^2-2y-1

We move all terms to the left:

0-(y^2-2y-1)=0

We add all the numbers together, and all the variables

-(y^2-2y-1)=0

We get rid of parentheses

-y^2+2y+1=0

We add all the numbers together, and all the variables

-1y^2+2y+1=0

a = -1; b = 2; c = +1;
Δ = b2-4ac
Δ = 22-4·(-1)·1
Δ = 8
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8}=\sqrt{4*2}=\sqrt{4}*\sqrt{2}=2\sqrt{2}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{2}}{2*-1}=\frac{-2-2\sqrt{2}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{2}}{2*-1}=\frac{-2+2\sqrt{2}}{-2}
$