U(x)=-2x2+8000x

Solution for U(x)=-2x2+8000x equation:

(U)=-2U^2+8000U

We move all terms to the left:

(U)-(-2U^2+8000U)=0

We get rid of parentheses

2U^2-8000U+U=0

We add all the numbers together, and all the variables

2U^2-7999U=0

a = 2; b = -7999; c = 0;
Δ = b2-4ac
Δ = -79992-4·2·0
Δ = 63984001
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$U_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$U_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{63984001}=7999$
$U_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7999)-7999}{2*2}=\frac{0}{4}
=0
$
$U_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7999)+7999}{2*2}=\frac{15998}{4}
=3999+1/2
$