4x(2x-4)=8

Solution for 4x(2x-4)=8 equation:

4x(2x-4)=8

We move all terms to the left:

4x(2x-4)-(8)=0

We multiply parentheses

8x^2-16x-8=0

a = 8; b = -16; c = -8;
Δ = b2-4ac
Δ = -162-4·8·(-8)
Δ = 512
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:

$\sqrt{\Delta}=\sqrt{512}=\sqrt{256*2}=\sqrt{256}*\sqrt{2}=16\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16\sqrt{2}}{2*8}=\frac{16-16\sqrt{2}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16\sqrt{2}}{2*8}=\frac{16+16\sqrt{2}}{16}
$