200x(360-2x)-1600=0

Solution for 200x(360-2x)-1600=0 equation:

200x(360-2x)-1600=0

We add all the numbers together, and all the variables

200x(-2x+360)-1600=0

We multiply parentheses

-400x^2+72000x-1600=0

a = -400; b = 72000; c = -1600;
Δ = b2-4ac
Δ = 720002-4·(-400)·(-1600)
Δ = 5181440000
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:

$\sqrt{\Delta}=\sqrt{5181440000}=\sqrt{10240000*506}=\sqrt{10240000}*\sqrt{506}=3200\sqrt{506}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72000)-3200\sqrt{506}}{2*-400}=\frac{-72000-3200\sqrt{506}}{-800}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72000)+3200\sqrt{506}}{2*-400}=\frac{-72000+3200\sqrt{506}}{-800}
$