x^2+200x-40000=0

Solution for x^2+200x-40000=0 equation:

x^2+200x-40000=0

a = 1; b = 200; c = -40000;
Δ = b2-4ac
Δ = 2002-4·1·(-40000)
Δ = 200000
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:

$\sqrt{\Delta}=\sqrt{200000}=\sqrt{40000*5}=\sqrt{40000}*\sqrt{5}=200\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-200\sqrt{5}}{2*1}=\frac{-200-200\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+200\sqrt{5}}{2*1}=\frac{-200+200\sqrt{5}}{2}
$