X^2+8000x=289000000

Solution for X^2+8000x=289000000 equation:

X^2+8000X=289000000

We move all terms to the left:

X^2+8000X-(289000000)=0

a = 1; b = 8000; c = -289000000;
Δ = b2-4ac
Δ = 80002-4·1·(-289000000)
Δ = 1220000000
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:

$\sqrt{\Delta}=\sqrt{1220000000}=\sqrt{4000000*305}=\sqrt{4000000}*\sqrt{305}=2000\sqrt{305}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8000)-2000\sqrt{305}}{2*1}=\frac{-8000-2000\sqrt{305}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8000)+2000\sqrt{305}}{2*1}=\frac{-8000+2000\sqrt{305}}{2}
$