200x-x^2=30x+600

Solution for 200x-x^2=30x+600 equation:

200x-x^2=30x+600

We move all terms to the left:

200x-x^2-(30x+600)=0

We add all the numbers together, and all the variables

-1x^2+200x-(30x+600)=0

We get rid of parentheses

-1x^2+200x-30x-600=0

We add all the numbers together, and all the variables

-1x^2+170x-600=0

a = -1; b = 170; c = -600;
Δ = b2-4ac
Δ = 1702-4·(-1)·(-600)
Δ = 26500
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:

$\sqrt{\Delta}=\sqrt{26500}=\sqrt{100*265}=\sqrt{100}*\sqrt{265}=10\sqrt{265}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(170)-10\sqrt{265}}{2*-1}=\frac{-170-10\sqrt{265}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(170)+10\sqrt{265}}{2*-1}=\frac{-170+10\sqrt{265}}{-2}
$