0=x^2+1x-1

Solution for 0=x^2+1x-1 equation:

0=x^2+1x-1

We move all terms to the left:

0-(x^2+1x-1)=0

We add all the numbers together, and all the variables

-(x^2+1x-1)=0

We get rid of parentheses

-x^2-1x+1=0

We add all the numbers together, and all the variables

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

a = -1; b = -1; c = +1;
Δ = b2-4ac
Δ = -12-4·(-1)·1
Δ = 5
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{5}}{2*-1}=\frac{1-\sqrt{5}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{5}}{2*-1}=\frac{1+\sqrt{5}}{-2}
$