U=-x2+1000x

Solution for U=-x2+1000x equation:

=-U2+1000U

We move all terms to the left:

-(-U2+1000U)=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

1U^2-1000U=0

We add all the numbers together, and all the variables

U^2-1000U=0

a = 1; b = -1000; c = 0;
Δ = b2-4ac
Δ = -10002-4·1·0
Δ = 1000000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$U_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$U_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1000000}=1000$
$U_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1000)-1000}{2*1}=\frac{0}{2}
=0
$
$U_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1000)+1000}{2*1}=\frac{2000}{2}
=1000
$