U=Y+20X-0.5x^2

Solution for U=Y+20X-0.5x^2 equation:

=+20U-0.5U^2

We move all terms to the left:

-(+20U-0.5U^2)=0

We get rid of parentheses

0.5U^2-20U=0

a = 0.5; b = -20; c = 0;
Δ = b2-4ac
Δ = -202-4·0.5·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$U_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$U_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$U_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20}{2*0.5}=\frac{0}{1}
=0
$
$U_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20}{2*0.5}=\frac{40}{1}
=40
$