1/5m=1/6m+1

Solution for 1/5m=1/6m+1 equation:

1/5m=1/6m+1

We move all terms to the left:

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


Domain of the equation: 5m!=0

m!=0/5

m!=0

m∈R



Domain of the equation: 6m+1)!=0

m∈R


We get rid of parentheses

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

We calculate fractions


6m/30m^2+(-5m)/30m^2-1=0

We multiply all the terms by the denominator


6m+(-5m)-1*30m^2=0

Wy multiply elements

-30m^2+6m+(-5m)=0

We get rid of parentheses

-30m^2+6m-5m=0

We add all the numbers together, and all the variables

-30m^2+m=0

a = -30; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-30)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-30}=\frac{-2}{-60}
=1/30
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-30}=\frac{0}{-60}
=0
$