1/3b+6=1/4b+8

Solution for 1/3b+6=1/4b+8 equation:

1/3b+6=1/4b+8

We move all terms to the left:

1/3b+6-(1/4b+8)=0


Domain of the equation: 3b!=0

b!=0/3

b!=0

b∈R



Domain of the equation: 4b+8)!=0

b∈R


We get rid of parentheses

1/3b-1/4b-8+6=0

We calculate fractions


4b/12b^2+(-3b)/12b^2-8+6=0

We add all the numbers together, and all the variables

4b/12b^2+(-3b)/12b^2-2=0

We multiply all the terms by the denominator


4b+(-3b)-2*12b^2=0

Wy multiply elements

-24b^2+4b+(-3b)=0

We get rid of parentheses

-24b^2+4b-3b=0

We add all the numbers together, and all the variables

-24b^2+b=0

a = -24; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-24)·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*-24}=\frac{-2}{-48}
=1/24
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-24}=\frac{0}{-48}
=0
$