F(x)=-x2+1000x

Solution for F(x)=-x2+1000x equation:

(F)=-F2+1000F

We move all terms to the left:

(F)-(-F2+1000F)=0

We add all the numbers together, and all the variables

-(-1F^2+1000F)+F=0

We get rid of parentheses

1F^2-1000F+F=0

We add all the numbers together, and all the variables

F^2-999F=0

a = 1; b = -999; c = 0;
Δ = b2-4ac
Δ = -9992-4·1·0
Δ = 998001
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{998001}=999$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-999)-999}{2*1}=\frac{0}{2}
=0
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-999)+999}{2*1}=\frac{1998}{2}
=999
$