F(5)=x^2-8x+20

Solution for F(5)=x^2-8x+20 equation:

(5)=F^2-8F+20

We move all terms to the left:

(5)-(F^2-8F+20)=0

We get rid of parentheses

-F^2+8F-20+5=0

We add all the numbers together, and all the variables

-1F^2+8F-15=0

a = -1; b = 8; c = -15;
Δ = b2-4ac
Δ = 82-4·(-1)·(-15)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2}{2*-1}=\frac{-10}{-2}
=+5
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2}{2*-1}=\frac{-6}{-2}
=+3
$