x^2+8x=8000

Solution for x^2+8x=8000 equation:

x^2+8x=8000

We move all terms to the left:

x^2+8x-(8000)=0

a = 1; b = 8; c = -8000;
Δ = b2-4ac
Δ = 82-4·1·(-8000)
Δ = 32064
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:

$\sqrt{\Delta}=\sqrt{32064}=\sqrt{64*501}=\sqrt{64}*\sqrt{501}=8\sqrt{501}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{501}}{2*1}=\frac{-8-8\sqrt{501}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{501}}{2*1}=\frac{-8+8\sqrt{501}}{2}
$