x^2-6000x-1000^2=0

Solution for x^2-6000x-1000^2=0 equation:

x^2-6000x-1000^2=0

We add all the numbers together, and all the variables

x^2-6000x-1000000=0

a = 1; b = -6000; c = -1000000;
Δ = b2-4ac
Δ = -60002-4·1·(-1000000)
Δ = 40000000
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:

$\sqrt{\Delta}=\sqrt{40000000}=\sqrt{4000000*10}=\sqrt{4000000}*\sqrt{10}=2000\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6000)-2000\sqrt{10}}{2*1}=\frac{6000-2000\sqrt{10}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6000)+2000\sqrt{10}}{2*1}=\frac{6000+2000\sqrt{10}}{2}
$