F(x)=-4x2+2x

Solution for F(x)=-4x2+2x equation:

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

We move all terms to the left:

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

We get rid of parentheses

4F^2-2F+F=0

We add all the numbers together, and all the variables

4F^2-1F=0

a = 4; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·4·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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