X2+200x-500=0

Solution for X2+200x-500=0 equation:

X2+200X-500=0

We add all the numbers together, and all the variables

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}
$