4800+40x=200x-x^2

Solution for 4800+40x=200x-x^2 equation:

4800+40x=200x-x^2

We move all terms to the left:

4800+40x-(200x-x^2)=0

We get rid of parentheses

x^2-200x+40x+4800=0

We add all the numbers together, and all the variables

x^2-160x+4800=0

a = 1; b = -160; c = +4800;
Δ = b2-4ac
Δ = -1602-4·1·4800
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-160)-80}{2*1}=\frac{80}{2}
=40
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-160)+80}{2*1}=\frac{240}{2}
=120
$