4=(8b)^2

Solution for 4=(8b)^2 equation:

4=(8b)^2

We move all terms to the left:

4-((8b)^2)=0

determiningTheFunctionDomain
-8b^2+4=0

a = -8; b = 0; c = +4;
Δ = b2-4ac
Δ = 02-4·(-8)·4
Δ = 128
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{128}=\sqrt{64*2}=\sqrt{64}*\sqrt{2}=8\sqrt{2}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{2}}{2*-8}=\frac{0-8\sqrt{2}}{-16}
=-\frac{8\sqrt{2}}{-16}
=-\frac{\sqrt{2}}{-2}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{2}}{2*-8}=\frac{0+8\sqrt{2}}{-16}
=\frac{8\sqrt{2}}{-16}
=\frac{\sqrt{2}}{-2}
$