x2-200x-4000=0

Solution for x2-200x-4000=0 equation:

x2-200x-4000=0

We add all the numbers together, and all the variables

x^2-200x-4000=0

a = 1; b = -200; c = -4000;
Δ = b2-4ac
Δ = -2002-4·1·(-4000)
Δ = 56000
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:

$\sqrt{\Delta}=\sqrt{56000}=\sqrt{1600*35}=\sqrt{1600}*\sqrt{35}=40\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-40\sqrt{35}}{2*1}=\frac{200-40\sqrt{35}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+40\sqrt{35}}{2*1}=\frac{200+40\sqrt{35}}{2}
$