F(x+1)=x^2

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

(F+1)=F^2

We move all terms to the left:

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

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

-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}
$