200x-2x^2=-x^2+40x+5500

Solution for 200x-2x^2=-x^2+40x+5500 equation:

200x-2x^2=-x^2+40x+5500

We move all terms to the left:

200x-2x^2-(-x^2+40x+5500)=0

We get rid of parentheses

-2x^2+x^2-40x+200x-5500=0

We add all the numbers together, and all the variables

-1x^2+160x-5500=0

a = -1; b = 160; c = -5500;
Δ = b2-4ac
Δ = 1602-4·(-1)·(-5500)
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(160)-60}{2*-1}=\frac{-220}{-2}
=+110
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(160)+60}{2*-1}=\frac{-100}{-2}
=+50
$