X^2+100x-8000=0

Solution for X^2+100x-8000=0 equation:

X^2+100X-8000=0

a = 1; b = 100; c = -8000;
Δ = b2-4ac
Δ = 1002-4·1·(-8000)
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{-(100)-20\sqrt{105}}{2*1}=\frac{-100-20\sqrt{105}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+20\sqrt{105}}{2*1}=\frac{-100+20\sqrt{105}}{2}
$