800=100x-0.5x^2-40x+800

Solution for 800=100x-0.5x^2-40x+800 equation:

800=100x-0.5x^2-40x+800

We move all terms to the left:

800-(100x-0.5x^2-40x+800)=0

We get rid of parentheses

0.5x^2-100x+40x-800+800=0

We add all the numbers together, and all the variables

0.5x^2-60x=0

a = 0.5; b = -60; c = 0;
Δ = b2-4ac
Δ = -602-4·0.5·0
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-60}{2*0.5}=\frac{0}{1}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+60}{2*0.5}=\frac{120}{1}
=120
$