5/6m-1/3-1/4m=41/3

Solution for 5/6m-1/3-1/4m=41/3 equation:

5/6m-1/3-1/4m=41/3

We move all terms to the left:

5/6m-1/3-1/4m-(41/3)=0


Domain of the equation: 6m!=0

m!=0/6

m!=0

m∈R



Domain of the equation: 4m!=0

m!=0/4

m!=0

m∈R


We add all the numbers together, and all the variables

5/6m-1/4m-1/3-(+41/3)=0

We get rid of parentheses

5/6m-1/4m-1/3-41/3=0

We calculate fractions


(-3936m^2-1)/216m^2+180m/216m^2+(-54m)/216m^2=0

We multiply all the terms by the denominator


(-3936m^2-1)+180m+(-54m)=0

We get rid of parentheses

-3936m^2+180m-54m-1=0

We add all the numbers together, and all the variables

-3936m^2+126m-1=0

a = -3936; b = 126; c = -1;
Δ = b2-4ac
Δ = 1262-4·(-3936)·(-1)
Δ = 132
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(126)-2\sqrt{33}}{2*-3936}=\frac{-126-2\sqrt{33}}{-7872}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(126)+2\sqrt{33}}{2*-3936}=\frac{-126+2\sqrt{33}}{-7872}
$