U(x)=-x2+400x-7500

Solution for U(x)=-x2+400x-7500 equation:

(U)=-U2+400U-7500

We move all terms to the left:

(U)-(-U2+400U-7500)=0

We add all the numbers together, and all the variables

-(-1U^2+400U-7500)+U=0

We get rid of parentheses

1U^2-400U+U+7500=0

We add all the numbers together, and all the variables

U^2-399U+7500=0

a = 1; b = -399; c = +7500;
Δ = b2-4ac
Δ = -3992-4·1·7500
Δ = 129201
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$U_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$U_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$U_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-399)-\sqrt{129201}}{2*1}=\frac{399-\sqrt{129201}}{2}
$
$U_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-399)+\sqrt{129201}}{2*1}=\frac{399+\sqrt{129201}}{2}
$