X(2x+200)=40000

Solution for X(2x+200)=40000 equation:

X(2X+200)=40000

We move all terms to the left:

X(2X+200)-(40000)=0

We multiply parentheses

2X^2+200X-40000=0

a = 2; b = 200; c = -40000;
Δ = b2-4ac
Δ = 2002-4·2·(-40000)
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*2}=\frac{-800}{4}
=-200
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+600}{2*2}=\frac{400}{4}
=100
$