0=u2-u-1

Solution for 0=u2-u-1 equation:

0=u2-u-1

We move all terms to the left:

0-(u2-u-1)=0

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

-u^2+1u+1=0

We add all the numbers together, and all the variables

-1u^2+u+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:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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