x^2-200x-800=0

Solution for x^2-200x-800=0 equation:

x^2-200x-800=0

a = 1; b = -200; c = -800;
Δ = b2-4ac
Δ = -2002-4·1·(-800)
Δ = 43200
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:

$\sqrt{\Delta}=\sqrt{43200}=\sqrt{14400*3}=\sqrt{14400}*\sqrt{3}=120\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-120\sqrt{3}}{2*1}=\frac{200-120\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+120\sqrt{3}}{2*1}=\frac{200+120\sqrt{3}}{2}
$