400=2x*(x-200)

Solution for 400=2x*(x-200) equation:

400=2x(x-200)

We move all terms to the left:

400-(2x(x-200))=0


We calculate terms in parentheses: -(2x(x-200)), so:

2x(x-200)

We multiply parentheses

2x^2-400x

Back to the equation:

-(2x^2-400x)


We get rid of parentheses

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

a = -2; b = 400; c = +400;
Δ = b2-4ac
Δ = 4002-4·(-2)·400
Δ = 163200
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:

$\sqrt{\Delta}=\sqrt{163200}=\sqrt{1600*102}=\sqrt{1600}*\sqrt{102}=40\sqrt{102}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(400)-40\sqrt{102}}{2*-2}=\frac{-400-40\sqrt{102}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(400)+40\sqrt{102}}{2*-2}=\frac{-400+40\sqrt{102}}{-4}
$