F(x)=x*x-1

Solution for F(x)=x*x-1 equation:

(F)=F*F-1

We move all terms to the left:

(F)-(F*F-1)=0

We get rid of parentheses

F-F*F+1=0

Wy multiply elements

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

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