0=(x^2)-200x+5000

Solution for 0=(x^2)-200x+5000 equation:

0=(x^2)-200x+5000

We move all terms to the left:

0-((x^2)-200x+5000)=0

We add all the numbers together, and all the variables

-(x^2-200x+5000)=0

We get rid of parentheses

-x^2+200x-5000=0

We add all the numbers together, and all the variables

-1x^2+200x-5000=0

a = -1; b = 200; c = -5000;
Δ = b2-4ac
Δ = 2002-4·(-1)·(-5000)
Δ = 20000
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:

$\sqrt{\Delta}=\sqrt{20000}=\sqrt{10000*2}=\sqrt{10000}*\sqrt{2}=100\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-100\sqrt{2}}{2*-1}=\frac{-200-100\sqrt{2}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+100\sqrt{2}}{2*-1}=\frac{-200+100\sqrt{2}}{-2}
$