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

We add all the numbers together, and all the variables

5m-10*6m^2=0

Wy multiply elements

-60m^2+5m=0

a = -60; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-60)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-60}=\frac{-10}{-120}
=1/12
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-60}=\frac{0}{-120}
=0
$