1200=1000x-200x^2

Solution for 1200=1000x-200x^2 equation:

1200=1000x-200x^2

We move all terms to the left:

1200-(1000x-200x^2)=0

We get rid of parentheses

200x^2-1000x+1200=0

a = 200; b = -1000; c = +1200;
Δ = b2-4ac
Δ = -10002-4·200·1200
Δ = 40000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{40000}=200$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1000)-200}{2*200}=\frac{800}{400}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1000)+200}{2*200}=\frac{1200}{400}
=3
$