4/m=6/3m+2

Solution for 4/m=6/3m+2 equation:

4/m=6/3m+2

We move all terms to the left:

4/m-(6/3m+2)=0


Domain of the equation: m!=0

m∈R



Domain of the equation: 3m+2)!=0

m∈R


We get rid of parentheses

4/m-6/3m-2=0

We calculate fractions


12m/3m^2+(-6m)/3m^2-2=0

We multiply all the terms by the denominator


12m+(-6m)-2*3m^2=0

Wy multiply elements

-6m^2+12m+(-6m)=0

We get rid of parentheses

-6m^2+12m-6m=0

We add all the numbers together, and all the variables

-6m^2+6m=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:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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