x^2-2x=5000

Solution for x^2-2x=5000 equation:

x^2-2x=5000

We move all terms to the left:

x^2-2x-(5000)=0

a = 1; b = -2; c = -5000;
Δ = b2-4ac
Δ = -22-4·1·(-5000)
Δ = 20004
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:

$\sqrt{\Delta}=\sqrt{20004}=\sqrt{4*5001}=\sqrt{4}*\sqrt{5001}=2\sqrt{5001}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{5001}}{2*1}=\frac{2-2\sqrt{5001}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{5001}}{2*1}=\frac{2+2\sqrt{5001}}{2}
$