200x-2x^2=-x^2+35+5750

Solution for 200x-2x^2=-x^2+35+5750 equation:

200x-2x^2=-x^2+35+5750

We move all terms to the left:

200x-2x^2-(-x^2+35+5750)=0

We get rid of parentheses

-2x^2+x^2+200x-35-5750=0

We add all the numbers together, and all the variables

-1x^2+200x-5785=0

a = -1; b = 200; c = -5785;
Δ = b2-4ac
Δ = 2002-4·(-1)·(-5785)
Δ = 16860
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{16860}=\sqrt{4*4215}=\sqrt{4}*\sqrt{4215}=2\sqrt{4215}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-2\sqrt{4215}}{2*-1}=\frac{-200-2\sqrt{4215}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+2\sqrt{4215}}{2*-1}=\frac{-200+2\sqrt{4215}}{-2}
$