x^2+200x+5000=0

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

x^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}
$