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

Solution for F(0)=4x^2-2x equation:

(0)=4F^2-2F

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

-4F^2+2F=0

a = -4; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-4)·0
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{-(2)-2}{2*-4}=\frac{-4}{-8}
=1/2
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-4}=\frac{0}{-8}
=0
$