3/4m-1/3m=10

Solution for 3/4m-1/3m=10 equation:

3/4m-1/3m=10

We move all terms to the left:

3/4m-1/3m-(10)=0


Domain of the equation: 4m!=0

m!=0/4

m!=0

m∈R



Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R


We calculate fractions


9m/12m^2+(-4m)/12m^2-10=0

We multiply all the terms by the denominator


9m+(-4m)-10*12m^2=0

Wy multiply elements

-120m^2+9m+(-4m)=0

We get rid of parentheses

-120m^2+9m-4m=0

We add all the numbers together, and all the variables

-120m^2+5m=0

a = -120; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-120)·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*-120}=\frac{-10}{-240}
=1/24
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-120}=\frac{0}{-240}
=0
$