F(4n)=4n^2-4n

Solution for F(4n)=4n^2-4n equation:

(4F)=4F^2-4F

We move all terms to the left:

(4F)-(4F^2-4F)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

-4F^2+8F=0

a = -4; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-4)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*-4}=\frac{-16}{-8}
=+2
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-4}=\frac{0}{-8}
=0
$