x(x-4)-12=8

Solution for x(x-4)-12=8 equation:

x(x-4)-12=8

We move all terms to the left:

x(x-4)-12-(8)=0

We add all the numbers together, and all the variables

x(x-4)-20=0

We multiply parentheses

x^2-4x-20=0

a = 1; b = -4; c = -20;
Δ = b2-4ac
Δ = -42-4·1·(-20)
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{6}}{2*1}=\frac{4-4\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{6}}{2*1}=\frac{4+4\sqrt{6}}{2}
$