F(0)=-x^2+x

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

(0)=-F^2+F

We move all terms to the left:

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

We add all the numbers together, and all the variables

-(-F^2+F)=0

We get rid of parentheses

F^2-F=0

We add all the numbers together, and all the variables

F^2-1F=0

a = 1; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·1·0
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*1}=\frac{0}{2}
=0
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*1}=\frac{2}{2}
=1
$