X^2-100x-18400=0

Solution for X^2-100x-18400=0 equation:

X^2-100X-18400=0

a = 1; b = -100; c = -18400;
Δ = b2-4ac
Δ = -1002-4·1·(-18400)
Δ = 83600
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:

$\sqrt{\Delta}=\sqrt{83600}=\sqrt{400*209}=\sqrt{400}*\sqrt{209}=20\sqrt{209}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-20\sqrt{209}}{2*1}=\frac{100-20\sqrt{209}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+20\sqrt{209}}{2*1}=\frac{100+20\sqrt{209}}{2}
$