-1/6m-5/8+3/4m=1/3

Solution for -1/6m-5/8+3/4m=1/3 equation:

-1/6m-5/8+3/4m=1/3

We move all terms to the left:

-1/6m-5/8+3/4m-(1/3)=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

-1/6m+3/4m-5/8-(+1/3)=0

We get rid of parentheses

-1/6m+3/4m-5/8-1/3=0

We calculate fractions


(-1440m^2)/4608m^2+(-768m^2)/4608m^2+(-768m)/4608m^2+3456m/4608m^2=0

We multiply all the terms by the denominator


(-1440m^2)+(-768m^2)+(-768m)+3456m=0

We add all the numbers together, and all the variables

(-1440m^2)+(-768m^2)+3456m+(-768m)=0

We get rid of parentheses

-1440m^2-768m^2+3456m-768m=0

We add all the numbers together, and all the variables

-2208m^2+2688m=0

a = -2208; b = 2688; c = 0;
Δ = b2-4ac
Δ = 26882-4·(-2208)·0
Δ = 7225344
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7225344}=2688$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2688)-2688}{2*-2208}=\frac{-5376}{-4416}
=1+5/23
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2688)+2688}{2*-2208}=\frac{0}{-4416}
=0
$