F(x)=x2-2x+1

Solution for F(x)=x2-2x+1 equation:

(F)=F2-2F+1

We move all terms to the left:

(F)-(F2-2F+1)=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

-F^2+2F+F-1=0

We add all the numbers together, and all the variables

-1F^2+3F-1=0

a = -1; b = 3; c = -1;
Δ = b2-4ac
Δ = 32-4·(-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:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{5}}{2*-1}=\frac{-3-\sqrt{5}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{5}}{2*-1}=\frac{-3+\sqrt{5}}{-2}
$