X^2-100x-200=0

Solution for X^2-100x-200=0 equation:

X^2-100X-200=0

a = 1; b = -100; c = -200;
Δ = b2-4ac
Δ = -1002-4·1·(-200)
Δ = 10800
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:

$\sqrt{\Delta}=\sqrt{10800}=\sqrt{3600*3}=\sqrt{3600}*\sqrt{3}=60\sqrt{3}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-60\sqrt{3}}{2*1}=\frac{100-60\sqrt{3}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+60\sqrt{3}}{2*1}=\frac{100+60\sqrt{3}}{2}
$