x(x-2)=800

Solution for x(x-2)=800 equation:

x(x-2)=800

We move all terms to the left:

x(x-2)-(800)=0

We multiply parentheses

x^2-2x-800=0

a = 1; b = -2; c = -800;
Δ = b2-4ac
Δ = -22-4·1·(-800)
Δ = 3204
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:

$\sqrt{\Delta}=\sqrt{3204}=\sqrt{36*89}=\sqrt{36}*\sqrt{89}=6\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-6\sqrt{89}}{2*1}=\frac{2-6\sqrt{89}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+6\sqrt{89}}{2*1}=\frac{2+6\sqrt{89}}{2}
$