x^2+4000x=8000000

Solution for x^2+4000x=8000000 equation:

x^2+4000x=8000000

We move all terms to the left:

x^2+4000x-(8000000)=0

a = 1; b = 4000; c = -8000000;
Δ = b2-4ac
Δ = 40002-4·1·(-8000000)
Δ = 48000000
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:

$\sqrt{\Delta}=\sqrt{48000000}=\sqrt{16000000*3}=\sqrt{16000000}*\sqrt{3}=4000\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4000)-4000\sqrt{3}}{2*1}=\frac{-4000-4000\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4000)+4000\sqrt{3}}{2*1}=\frac{-4000+4000\sqrt{3}}{2}
$