200x-2x^2=-x^2+15x+8050

Solution for 200x-2x^2=-x^2+15x+8050 equation:

200x-2x^2=-x^2+15x+8050

We move all terms to the left:

200x-2x^2-(-x^2+15x+8050)=0

We get rid of parentheses

-2x^2+x^2-15x+200x-8050=0

We add all the numbers together, and all the variables

-1x^2+185x-8050=0

a = -1; b = 185; c = -8050;
Δ = b2-4ac
Δ = 1852-4·(-1)·(-8050)
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(185)-45}{2*-1}=\frac{-230}{-2}
=+115
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(185)+45}{2*-1}=\frac{-140}{-2}
=+70
$