4x(x-2)=16

Solution for 4x(x-2)=16 equation:

4x(x-2)=16

We move all terms to the left:

4x(x-2)-(16)=0

We multiply parentheses

4x^2-8x-16=0

a = 4; b = -8; c = -16;
Δ = b2-4ac
Δ = -82-4·4·(-16)
Δ = 320
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:

$\sqrt{\Delta}=\sqrt{320}=\sqrt{64*5}=\sqrt{64}*\sqrt{5}=8\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{5}}{2*4}=\frac{8-8\sqrt{5}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{5}}{2*4}=\frac{8+8\sqrt{5}}{8}
$