x^2+500x+10000=0

Solution for x^2+500x+10000=0 equation:

x^2+500x+10000=0

a = 1; b = 500; c = +10000;
Δ = b2-4ac
Δ = 5002-4·1·10000
Δ = 210000
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:

$\sqrt{\Delta}=\sqrt{210000}=\sqrt{10000*21}=\sqrt{10000}*\sqrt{21}=100\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(500)-100\sqrt{21}}{2*1}=\frac{-500-100\sqrt{21}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(500)+100\sqrt{21}}{2*1}=\frac{-500+100\sqrt{21}}{2}
$