4s^2-16s=16

Solution for 4s^2-16s=16 equation:

4s^2-16s=16

We move all terms to the left:

4s^2-16s-(16)=0

a = 4; b = -16; c = -16;
Δ = b2-4ac
Δ = -162-4·4·(-16)
Δ = 512
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{512}=\sqrt{256*2}=\sqrt{256}*\sqrt{2}=16\sqrt{2}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16\sqrt{2}}{2*4}=\frac{16-16\sqrt{2}}{8}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16\sqrt{2}}{2*4}=\frac{16+16\sqrt{2}}{8}
$