3/3b+4=7/b-4

Solution for 3/3b+4=7/b-4 equation:

3/3b+4=7/b-4

We move all terms to the left:

3/3b+4-(7/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

3/3b-7/b+4+4=0

We calculate fractions


3b/3b^2+(-21b)/3b^2+4+4=0

We add all the numbers together, and all the variables

3b/3b^2+(-21b)/3b^2+8=0

We multiply all the terms by the denominator


3b+(-21b)+8*3b^2=0

Wy multiply elements

24b^2+3b+(-21b)=0

We get rid of parentheses

24b^2+3b-21b=0

We add all the numbers together, and all the variables

24b^2-18b=0

a = 24; b = -18; c = 0;
Δ = b2-4ac
Δ = -182-4·24·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18}{2*24}=\frac{0}{48}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18}{2*24}=\frac{36}{48}
=3/4
$