2x(-2x+8)=4

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

2x(-2x+8)=4

We move all terms to the left:

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

We multiply parentheses

-4x^2+16x-4=0

a = -4; b = 16; c = -4;
Δ = b2-4ac
Δ = 162-4·(-4)·(-4)
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-8\sqrt{3}}{2*-4}=\frac{-16-8\sqrt{3}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+8\sqrt{3}}{2*-4}=\frac{-16+8\sqrt{3}}{-8}
$