x^2+100x-75000=0

Solution for x^2+100x-75000=0 equation:

x^2+100x-75000=0

a = 1; b = 100; c = -75000;
Δ = b2-4ac
Δ = 1002-4·1·(-75000)
Δ = 310000
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:

$\sqrt{\Delta}=\sqrt{310000}=\sqrt{10000*31}=\sqrt{10000}*\sqrt{31}=100\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-100\sqrt{31}}{2*1}=\frac{-100-100\sqrt{31}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+100\sqrt{31}}{2*1}=\frac{-100+100\sqrt{31}}{2}
$