1/m-6=14/2m

Solution for 1/m-6=14/2m equation:

1/m-6=14/2m

We move all terms to the left:

1/m-6-(14/2m)=0


Domain of the equation: 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/m-(+14/2m)-6=0

We get rid of parentheses

1/m-14/2m-6=0

We calculate fractions


2m/2m^2+(-14m)/2m^2-6=0

We multiply all the terms by the denominator


2m+(-14m)-6*2m^2=0

Wy multiply elements

-12m^2+2m+(-14m)=0

We get rid of parentheses

-12m^2+2m-14m=0

We add all the numbers together, and all the variables

-12m^2-12m=0

a = -12; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·(-12)·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*-12}=\frac{0}{-24}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*-12}=\frac{24}{-24}
=-1
$