1/2m-1/3m=10

Solution for 1/2m-1/3m=10 equation:

1/2m-1/3m=10

We move all terms to the left:

1/2m-1/3m-(10)=0


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R



Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R


We calculate fractions


3m/6m^2+(-2m)/6m^2-10=0

We multiply all the terms by the denominator


3m+(-2m)-10*6m^2=0

Wy multiply elements

-60m^2+3m+(-2m)=0

We get rid of parentheses

-60m^2+3m-2m=0

We add all the numbers together, and all the variables

-60m^2+m=0

a = -60; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-60)·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*-60}=\frac{-2}{-120}
=1/60
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-60}=\frac{0}{-120}
=0
$