F(5)=4x^2-2x

Solution for F(5)=4x^2-2x equation:

(5)=4F^2-2F

We move all terms to the left:

(5)-(4F^2-2F)=0

We get rid of parentheses

-4F^2+2F+5=0

a = -4; b = 2; c = +5;
Δ = b2-4ac
Δ = 22-4·(-4)·5
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{21}}{2*-4}=\frac{-2-2\sqrt{21}}{-8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{21}}{2*-4}=\frac{-2+2\sqrt{21}}{-8}
$