F(5)=x^2-6x+11

Solution for F(5)=x^2-6x+11 equation:

(5)=F^2-6F+11

We move all terms to the left:

(5)-(F^2-6F+11)=0

We get rid of parentheses

-F^2+6F-11+5=0

We add all the numbers together, and all the variables

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

a = -1; b = 6; c = -6;
Δ = b2-4ac
Δ = 62-4·(-1)·(-6)
Δ = 12
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{3}}{2*-1}=\frac{-6-2\sqrt{3}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{3}}{2*-1}=\frac{-6+2\sqrt{3}}{-2}
$