x(x-6)=2

Solution for x(x-6)=2 equation:

x(x-6)=2

We move all terms to the left:

x(x-6)-(2)=0

We multiply parentheses

x^2-6x-2=0

a = 1; b = -6; c = -2;
Δ = b2-4ac
Δ = -62-4·1·(-2)
Δ = 44
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:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{11}}{2*1}=\frac{6-2\sqrt{11}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{11}}{2*1}=\frac{6+2\sqrt{11}}{2}
$