2b-1/2b=30

Solution for 2b-1/2b=30 equation:

2b-1/2b=30

We move all terms to the left:

2b-1/2b-(30)=0


Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R


We multiply all the terms by the denominator


2b*2b-30*2b-1=0

Wy multiply elements

4b^2-60b-1=0

a = 4; b = -60; c = -1;
Δ = b2-4ac
Δ = -602-4·4·(-1)
Δ = 3616
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:

$\sqrt{\Delta}=\sqrt{3616}=\sqrt{16*226}=\sqrt{16}*\sqrt{226}=4\sqrt{226}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-4\sqrt{226}}{2*4}=\frac{60-4\sqrt{226}}{8}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+4\sqrt{226}}{2*4}=\frac{60+4\sqrt{226}}{8}
$