x*(x-1)=5000

Solution for x*(x-1)=5000 equation:

x(x-1)=5000

We move all terms to the left:

x(x-1)-(5000)=0

We multiply parentheses

x^2-1x-5000=0

a = 1; b = -1; c = -5000;
Δ = b2-4ac
Δ = -12-4·1·(-5000)
Δ = 20001
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{20001}}{2*1}=\frac{1-\sqrt{20001}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{20001}}{2*1}=\frac{1+\sqrt{20001}}{2}
$