2x(200-x)=200

Solution for 2x(200-x)=200 equation:

2x(200-x)=200

We move all terms to the left:

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

We add all the numbers together, and all the variables

2x(-1x+200)-200=0

We multiply parentheses

-2x^2+400x-200=0

a = -2; b = 400; c = -200;
Δ = b2-4ac
Δ = 4002-4·(-2)·(-200)
Δ = 158400
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:

$\sqrt{\Delta}=\sqrt{158400}=\sqrt{14400*11}=\sqrt{14400}*\sqrt{11}=120\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(400)-120\sqrt{11}}{2*-2}=\frac{-400-120\sqrt{11}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(400)+120\sqrt{11}}{2*-2}=\frac{-400+120\sqrt{11}}{-4}
$