X(x-2)=3500

Solution for X(x-2)=3500 equation:

X(X-2)=3500

We move all terms to the left:

X(X-2)-(3500)=0

We multiply parentheses

X^2-2X-3500=0

a = 1; b = -2; c = -3500;
Δ = b2-4ac
Δ = -22-4·1·(-3500)
Δ = 14004
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:

$\sqrt{\Delta}=\sqrt{14004}=\sqrt{36*389}=\sqrt{36}*\sqrt{389}=6\sqrt{389}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-6\sqrt{389}}{2*1}=\frac{2-6\sqrt{389}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+6\sqrt{389}}{2*1}=\frac{2+6\sqrt{389}}{2}
$