200x^2+200x=400

Solution for 200x^2+200x=400 equation:

200x^2+200x=400

We move all terms to the left:

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

a = 200; b = 200; c = -400;
Δ = b2-4ac
Δ = 2002-4·200·(-400)
Δ = 360000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{360000}=600$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-600}{2*200}=\frac{-800}{400}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+600}{2*200}=\frac{400}{400}
=1
$