2b+4/2b=16

Solution for 2b+4/2b=16 equation:

2b+4/2b=16

We move all terms to the left:

2b+4/2b-(16)=0


Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R


We multiply all the terms by the denominator


2b*2b-16*2b+4=0

Wy multiply elements

4b^2-32b+4=0

a = 4; b = -32; c = +4;
Δ = b2-4ac
Δ = -322-4·4·4
Δ = 960
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:

$\sqrt{\Delta}=\sqrt{960}=\sqrt{64*15}=\sqrt{64}*\sqrt{15}=8\sqrt{15}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-8\sqrt{15}}{2*4}=\frac{32-8\sqrt{15}}{8}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+8\sqrt{15}}{2*4}=\frac{32+8\sqrt{15}}{8}
$