x2+2x-15000=109000

Solution for x2+2x-15000=109000 equation:

x2+2x-15000=109000

We move all terms to the left:

x2+2x-15000-(109000)=0

We add all the numbers together, and all the variables

x^2+2x-124000=0

a = 1; b = 2; c = -124000;
Δ = b2-4ac
Δ = 22-4·1·(-124000)
Δ = 496004
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:

$\sqrt{\Delta}=\sqrt{496004}=\sqrt{4*124001}=\sqrt{4}*\sqrt{124001}=2\sqrt{124001}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{124001}}{2*1}=\frac{-2-2\sqrt{124001}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{124001}}{2*1}=\frac{-2+2\sqrt{124001}}{2}
$