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!=0

m∈R



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

m∈R


We get rid of parentheses

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

We calculate fractions


9m/3m^2+(-6m)/3m^2-8-1=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-27m^2+9m+(-6m)=0

We get rid of parentheses

-27m^2+9m-6m=0

We add all the numbers together, and all the variables

-27m^2+3m=0

a = -27; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-27)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*-27}=\frac{-6}{-54}
=1/9
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-27}=\frac{0}{-54}
=0
$