x^2+100x-12000=0

Solution for x^2+100x-12000=0 equation:

x^2+100x-12000=0

a = 1; b = 100; c = -12000;
Δ = b2-4ac
Δ = 1002-4·1·(-12000)
Δ = 58000
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:

$\sqrt{\Delta}=\sqrt{58000}=\sqrt{400*145}=\sqrt{400}*\sqrt{145}=20\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-20\sqrt{145}}{2*1}=\frac{-100-20\sqrt{145}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+20\sqrt{145}}{2*1}=\frac{-100+20\sqrt{145}}{2}
$