x(x-6)=800

Solution for x(x-6)=800 equation:

x(x-6)=800

We move all terms to the left:

x(x-6)-(800)=0

We multiply parentheses

x^2-6x-800=0

a = 1; b = -6; c = -800;
Δ = b2-4ac
Δ = -62-4·1·(-800)
Δ = 3236
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:

$\sqrt{\Delta}=\sqrt{3236}=\sqrt{4*809}=\sqrt{4}*\sqrt{809}=2\sqrt{809}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{809}}{2*1}=\frac{6-2\sqrt{809}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{809}}{2*1}=\frac{6+2\sqrt{809}}{2}
$