x^2-16x=2000

Solution for x^2-16x=2000 equation:

x^2-16x=2000

We move all terms to the left:

x^2-16x-(2000)=0

a = 1; b = -16; c = -2000;
Δ = b2-4ac
Δ = -162-4·1·(-2000)
Δ = 8256
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:

$\sqrt{\Delta}=\sqrt{8256}=\sqrt{64*129}=\sqrt{64}*\sqrt{129}=8\sqrt{129}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-8\sqrt{129}}{2*1}=\frac{16-8\sqrt{129}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+8\sqrt{129}}{2*1}=\frac{16+8\sqrt{129}}{2}
$