x^2+2x=99999

Solution for x^2+2x=99999 equation:

x^2+2x=99999

We move all terms to the left:

x^2+2x-(99999)=0

a = 1; b = 2; c = -99999;
Δ = b2-4ac
Δ = 22-4·1·(-99999)
Δ = 400000
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:

$\sqrt{\Delta}=\sqrt{400000}=\sqrt{40000*10}=\sqrt{40000}*\sqrt{10}=200\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-200\sqrt{10}}{2*1}=\frac{-2-200\sqrt{10}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+200\sqrt{10}}{2*1}=\frac{-2+200\sqrt{10}}{2}
$