200x-2x^2=-x^2+25x+6250

Solution for 200x-2x^2=-x^2+25x+6250 equation:

200x-2x^2=-x^2+25x+6250

We move all terms to the left:

200x-2x^2-(-x^2+25x+6250)=0

We get rid of parentheses

-2x^2+x^2-25x+200x-6250=0

We add all the numbers together, and all the variables

-1x^2+175x-6250=0

a = -1; b = 175; c = -6250;
Δ = b2-4ac
Δ = 1752-4·(-1)·(-6250)
Δ = 5625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5625}=75$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(175)-75}{2*-1}=\frac{-250}{-2}
=+125
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(175)+75}{2*-1}=\frac{-100}{-2}
=+50
$