8/3b+4=2/b-4

Solution for 8/3b+4=2/b-4 equation:

8/3b+4=2/b-4

We move all terms to the left:

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


Domain of the equation: 3b!=0

b!=0/3

b!=0

b∈R



Domain of the equation: b-4)!=0

b∈R


We get rid of parentheses

8/3b-2/b+4+4=0

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

24b^2+8b+(-6b)=0

We get rid of parentheses

24b^2+8b-6b=0

We add all the numbers together, and all the variables

24b^2+2b=0

a = 24; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·24·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*24}=\frac{-4}{48}
=-1/12
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*24}=\frac{0}{48}
=0
$