-600x-x^2=600

Solution for -600x-x^2=600 equation:

-600x-x^2=600

We move all terms to the left:

-600x-x^2-(600)=0

We add all the numbers together, and all the variables

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

a = -1; b = -600; c = -600;
Δ = b2-4ac
Δ = -6002-4·(-1)·(-600)
Δ = 357600
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:

$\sqrt{\Delta}=\sqrt{357600}=\sqrt{400*894}=\sqrt{400}*\sqrt{894}=20\sqrt{894}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-600)-20\sqrt{894}}{2*-1}=\frac{600-20\sqrt{894}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-600)+20\sqrt{894}}{2*-1}=\frac{600+20\sqrt{894}}{-2}
$