-1/3m-1/2=2+1/4m

Solution for -1/3m-1/2=2+1/4m equation:

-1/3m-1/2=2+1/4m

We move all terms to the left:

-1/3m-1/2-(2+1/4m)=0


Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R



Domain of the equation: 4m)!=0

m!=0/1

m!=0

m∈R


We add all the numbers together, and all the variables

-1/3m-(1/4m+2)-1/2=0

We get rid of parentheses

-1/3m-1/4m-2-1/2=0

We calculate fractions


(-48m^2)/48m^2+(-16m)/48m^2+(-12m)/48m^2-2=0

We multiply all the terms by the denominator


(-48m^2)+(-16m)+(-12m)-2*48m^2=0

Wy multiply elements

(-48m^2)-96m^2+(-16m)+(-12m)=0

We get rid of parentheses

-48m^2-96m^2-16m-12m=0

We add all the numbers together, and all the variables

-144m^2-28m=0

a = -144; b = -28; c = 0;
Δ = b2-4ac
Δ = -282-4·(-144)·0
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-28}{2*-144}=\frac{0}{-288}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+28}{2*-144}=\frac{56}{-288}
=-7/36
$