U(x)=-2x^2+150x-800

Solution for U(x)=-2x^2+150x-800 equation:

(U)=-2U^2+150U-800

We move all terms to the left:

(U)-(-2U^2+150U-800)=0

We get rid of parentheses

2U^2-150U+U+800=0

We add all the numbers together, and all the variables

2U^2-149U+800=0

a = 2; b = -149; c = +800;
Δ = b2-4ac
Δ = -1492-4·2·800
Δ = 15801
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{-(-149)-\sqrt{15801}}{2*2}=\frac{149-\sqrt{15801}}{4}
$
$U_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-149)+\sqrt{15801}}{2*2}=\frac{149+\sqrt{15801}}{4}
$