x(x-18)-6(x-8)=0

Solution for x(x-18)-6(x-8)=0 equation:

x(x-18)-6(x-8)=0

We multiply parentheses

x^2-18x-6x+48=0

We add all the numbers together, and all the variables

x^2-24x+48=0

a = 1; b = -24; c = +48;
Δ = b2-4ac
Δ = -242-4·1·48
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-8\sqrt{6}}{2*1}=\frac{24-8\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+8\sqrt{6}}{2*1}=\frac{24+8\sqrt{6}}{2}
$