10000+x^2+200x=10005

Solution for 10000+x^2+200x=10005 equation:

10000+x^2+200x=10005

We move all terms to the left:

10000+x^2+200x-(10005)=0

We add all the numbers together, and all the variables

x^2+200x-5=0

a = 1; b = 200; c = -5;
Δ = b2-4ac
Δ = 2002-4·1·(-5)
Δ = 40020
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:

$\sqrt{\Delta}=\sqrt{40020}=\sqrt{4*10005}=\sqrt{4}*\sqrt{10005}=2\sqrt{10005}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-2\sqrt{10005}}{2*1}=\frac{-200-2\sqrt{10005}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+2\sqrt{10005}}{2*1}=\frac{-200+2\sqrt{10005}}{2}
$