1/2b+2b=20

Solution for 1/2b+2b=20 equation:

1/2b+2b=20

We move all terms to the left:

1/2b+2b-(20)=0


Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R


We add all the numbers together, and all the variables

2b+1/2b-20=0

We multiply all the terms by the denominator


2b*2b-20*2b+1=0

Wy multiply elements

4b^2-40b+1=0

a = 4; b = -40; c = +1;
Δ = b2-4ac
Δ = -402-4·4·1
Δ = 1584
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:

$\sqrt{\Delta}=\sqrt{1584}=\sqrt{144*11}=\sqrt{144}*\sqrt{11}=12\sqrt{11}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-12\sqrt{11}}{2*4}=\frac{40-12\sqrt{11}}{8}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+12\sqrt{11}}{2*4}=\frac{40+12\sqrt{11}}{8}
$