3/3b-6=-1/b-4

Solution for 3/3b-6=-1/b-4 equation:

3/3b-6=-1/b-4

We move all terms to the left:

3/3b-6-(-1/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+1/b+4-6=0

We calculate fractions


3b/3b^2+3b/3b^2+4-6=0

We add all the numbers together, and all the variables

3b/3b^2+3b/3b^2-2=0

We multiply all the terms by the denominator


3b+3b-2*3b^2=0

We add all the numbers together, and all the variables

6b-2*3b^2=0

Wy multiply elements

-6b^2+6b=0

a = -6; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-6)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-6}=\frac{-12}{-12}
=1
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-6}=\frac{0}{-12}
=0
$