F(3)=x2-5x+1

Solution for F(3)=x2-5x+1 equation:

(3)=F2-5F+1

We move all terms to the left:

(3)-(F2-5F+1)=0

We add all the numbers together, and all the variables

-(+F^2-5F+1)+3=0

We get rid of parentheses

-F^2+5F-1+3=0

We add all the numbers together, and all the variables

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

a = -1; b = 5; c = +2;
Δ = b2-4ac
Δ = 52-4·(-1)·2
Δ = 33
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{33}}{2*-1}=\frac{-5-\sqrt{33}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{33}}{2*-1}=\frac{-5+\sqrt{33}}{-2}
$