0=x^2+5000x-500

Solution for 0=x^2+5000x-500 equation:

0=x^2+5000x-500

We move all terms to the left:

0-(x^2+5000x-500)=0

We add all the numbers together, and all the variables

-(x^2+5000x-500)=0

We get rid of parentheses

-x^2-5000x+500=0

We add all the numbers together, and all the variables

-1x^2-5000x+500=0

a = -1; b = -5000; c = +500;
Δ = b2-4ac
Δ = -50002-4·(-1)·500
Δ = 25002000
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:

$\sqrt{\Delta}=\sqrt{25002000}=\sqrt{3600*6945}=\sqrt{3600}*\sqrt{6945}=60\sqrt{6945}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5000)-60\sqrt{6945}}{2*-1}=\frac{5000-60\sqrt{6945}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5000)+60\sqrt{6945}}{2*-1}=\frac{5000+60\sqrt{6945}}{-2}
$