F(x+1)=x2-4x+6

Solution for F(x+1)=x2-4x+6 equation:

(F+1)=F2-4F+6

We move all terms to the left:

(F+1)-(F2-4F+6)=0

We add all the numbers together, and all the variables

-(+F^2-4F+6)+(F+1)=0

We get rid of parentheses

-F^2+4F+F-6+1=0

We add all the numbers together, and all the variables

-1F^2+5F-5=0

a = -1; b = 5; c = -5;
Δ = b2-4ac
Δ = 52-4·(-1)·(-5)
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{-(5)-\sqrt{5}}{2*-1}=\frac{-5-\sqrt{5}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{5}}{2*-1}=\frac{-5+\sqrt{5}}{-2}
$