2b+1/2b-5=50+1/2b

Solution for 2b+1/2b-5=50+1/2b equation:

2b+1/2b-5=50+1/2b

We move all terms to the left:

2b+1/2b-5-(50+1/2b)=0


Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R



Domain of the equation: 2b)!=0

b!=0/1

b!=0

b∈R


We add all the numbers together, and all the variables

2b+1/2b-(1/2b+50)-5=0

We get rid of parentheses

2b+1/2b-1/2b-50-5=0

We multiply all the terms by the denominator


2b*2b-50*2b-5*2b+1-1=0

We add all the numbers together, and all the variables

2b*2b-50*2b-5*2b=0

Wy multiply elements

4b^2-100b-10b=0

We add all the numbers together, and all the variables

4b^2-110b=0

a = 4; b = -110; c = 0;
Δ = b2-4ac
Δ = -1102-4·4·0
Δ = 12100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12100}=110$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-110)-110}{2*4}=\frac{0}{8}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-110)+110}{2*4}=\frac{220}{8}
=27+1/2
$