3/(m-1)=6/3m+8

Solution for 3/(m-1)=6/3m+8 equation:

3/(m-1)=6/3m+8

We move all terms to the left:

3/(m-1)-(6/3m+8)=0


Domain of the equation: (m-1)!=0

We move all terms containing m to the left, all other terms to the right

m!=1

m∈R



Domain of the equation: 3m+8)!=0

m∈R


We get rid of parentheses

3/(m-1)-6/3m-8=0

We calculate fractions


9m/(3m^2-3m)+(-6m+6)/(3m^2-3m)-8=0

We multiply all the terms by the denominator


9m+(-6m+6)-8*(3m^2-3m)=0

We multiply parentheses

-24m^2+9m+(-6m+6)+24m=0

We get rid of parentheses

-24m^2+9m-6m+24m+6=0

We add all the numbers together, and all the variables

-24m^2+27m+6=0

a = -24; b = 27; c = +6;
Δ = b2-4ac
Δ = 272-4·(-24)·6
Δ = 1305
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1305}=\sqrt{9*145}=\sqrt{9}*\sqrt{145}=3\sqrt{145}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-3\sqrt{145}}{2*-24}=\frac{-27-3\sqrt{145}}{-48}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+3\sqrt{145}}{2*-24}=\frac{-27+3\sqrt{145}}{-48}
$