200x-2x^2=-x^2+35x+6050

Solution for 200x-2x^2=-x^2+35x+6050 equation:

200x-2x^2=-x^2+35x+6050

We move all terms to the left:

200x-2x^2-(-x^2+35x+6050)=0

We get rid of parentheses

-2x^2+x^2-35x+200x-6050=0

We add all the numbers together, and all the variables

-1x^2+165x-6050=0

a = -1; b = 165; c = -6050;
Δ = b2-4ac
Δ = 1652-4·(-1)·(-6050)
Δ = 3025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3025}=55$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(165)-55}{2*-1}=\frac{-220}{-2}
=+110
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(165)+55}{2*-1}=\frac{-110}{-2}
=+55
$