200x-x^2=2275

Solution for 200x-x^2=2275 equation:

200x-x^2=2275

We move all terms to the left:

200x-x^2-(2275)=0

We add all the numbers together, and all the variables

-1x^2+200x-2275=0

a = -1; b = 200; c = -2275;
Δ = b2-4ac
Δ = 2002-4·(-1)·(-2275)
Δ = 30900
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:

$\sqrt{\Delta}=\sqrt{30900}=\sqrt{100*309}=\sqrt{100}*\sqrt{309}=10\sqrt{309}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-10\sqrt{309}}{2*-1}=\frac{-200-10\sqrt{309}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+10\sqrt{309}}{2*-1}=\frac{-200+10\sqrt{309}}{-2}
$