0=8000+200x-0.2x^2

Solution for 0=8000+200x-0.2x^2 equation:

0=8000+200x-0.2x^2

We move all terms to the left:

0-(8000+200x-0.2x^2)=0

We add all the numbers together, and all the variables

-(8000+200x-0.2x^2)=0

We get rid of parentheses

0.2x^2-200x-8000=0

a = 0.2; b = -200; c = -8000;
Δ = b2-4ac
Δ = -2002-4·0.2·(-8000)
Δ = 46400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{46400}=\sqrt{1600*29}=\sqrt{1600}*\sqrt{29}=40\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-40\sqrt{29}}{2*0.2}=\frac{200-40\sqrt{29}}{0.4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+40\sqrt{29}}{2*0.2}=\frac{200+40\sqrt{29}}{0.4}
$