U=-0.002x^2+50x-180000

Solution for U=-0.002x^2+50x-180000 equation:

=-0.002U^2+50U-180000

We move all terms to the left:

-(-0.002U^2+50U-180000)=0

We get rid of parentheses

0.002U^2-50U+180000=0

a = 0.002; b = -50; c = +180000;
Δ = b2-4ac
Δ = -502-4·0.002·180000
Δ = 1060
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$U_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$U_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1060}=\sqrt{4*265}=\sqrt{4}*\sqrt{265}=2\sqrt{265}$
$U_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{265}}{2*0.002}=\frac{50-2\sqrt{265}}{0.004}
$
$U_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{265}}{2*0.002}=\frac{50+2\sqrt{265}}{0.004}
$