2/m+1/6=4/3m

Solution for 2/m+1/6=4/3m equation:

2/m+1/6=4/3m

We move all terms to the left:

2/m+1/6-(4/3m)=0


Domain of the equation: m!=0

m∈R



Domain of the equation: 3m)!=0

m!=0/1

m!=0

m∈R


We add all the numbers together, and all the variables

2/m-(+4/3m)+1/6=0

We get rid of parentheses

2/m-4/3m+1/6=0

We calculate fractions


9m^2/108m^2+216m/108m^2+(-144m)/108m^2=0

We multiply all the terms by the denominator


9m^2+216m+(-144m)=0

We get rid of parentheses

9m^2+216m-144m=0

We add all the numbers together, and all the variables

9m^2+72m=0

a = 9; b = 72; c = 0;
Δ = b2-4ac
Δ = 722-4·9·0
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-72}{2*9}=\frac{-144}{18}
=-8
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+72}{2*9}=\frac{0}{18}
=0
$