x^2-200*x-500=0

Solution for x^2-200*x-500=0 equation:

x^2-200x-500=0

a = 1; b = -200; c = -500;
Δ = b2-4ac
Δ = -2002-4·1·(-500)
Δ = 42000
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:

$\sqrt{\Delta}=\sqrt{42000}=\sqrt{400*105}=\sqrt{400}*\sqrt{105}=20\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-20\sqrt{105}}{2*1}=\frac{200-20\sqrt{105}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+20\sqrt{105}}{2*1}=\frac{200+20\sqrt{105}}{2}
$