1/2b=2/3b-8

Solution for 1/2b=2/3b-8 equation:

1/2b=2/3b-8

We move all terms to the left:

1/2b-(2/3b-8)=0


Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R



Domain of the equation: 3b-8)!=0

b∈R


We get rid of parentheses

1/2b-2/3b+8=0

We calculate fractions


3b/6b^2+(-4b)/6b^2+8=0

We multiply all the terms by the denominator


3b+(-4b)+8*6b^2=0

Wy multiply elements

48b^2+3b+(-4b)=0

We get rid of parentheses

48b^2+3b-4b=0

We add all the numbers together, and all the variables

48b^2-1b=0

a = 48; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·48·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*48}=\frac{0}{96}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*48}=\frac{2}{96}
=1/48
$