1/6m-5=1/2m

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

1/6m-5=1/2m

We move all terms to the left:

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


Domain of the equation: 6m!=0

m!=0/6

m!=0

m∈R



Domain of the equation: 2m)!=0

m!=0/1

m!=0

m∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


2m/12m^2+(-6m)/12m^2-5=0

We multiply all the terms by the denominator


2m+(-6m)-5*12m^2=0

Wy multiply elements

-60m^2+2m+(-6m)=0

We get rid of parentheses

-60m^2+2m-6m=0

We add all the numbers together, and all the variables

-60m^2-4m=0

a = -60; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-60)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*-60}=\frac{0}{-120}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-60}=\frac{8}{-120}
=-1/15
$