1/6-2/5m=1/6m-2

Solution for 1/6-2/5m=1/6m-2 equation:

1/6-2/5m=1/6m-2

We move all terms to the left:

1/6-2/5m-(1/6m-2)=0


Domain of the equation: 5m!=0

m!=0/5

m!=0

m∈R



Domain of the equation: 6m-2)!=0

m∈R


We get rid of parentheses

-2/5m-1/6m+2+1/6=0

We calculate fractions


(-432m)/1080m^2+(-5m)/1080m^2+5m/1080m^2+2=0

We multiply all the terms by the denominator


(-432m)+(-5m)+5m+2*1080m^2=0

We add all the numbers together, and all the variables

5m+(-432m)+(-5m)+2*1080m^2=0

Wy multiply elements

2160m^2+5m+(-432m)+(-5m)=0

We get rid of parentheses

2160m^2+5m-432m-5m=0

We add all the numbers together, and all the variables

2160m^2-432m=0

a = 2160; b = -432; c = 0;
Δ = b2-4ac
Δ = -4322-4·2160·0
Δ = 186624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{186624}=432$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-432)-432}{2*2160}=\frac{0}{4320}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-432)+432}{2*2160}=\frac{864}{4320}
=1/5
$