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

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

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

We move all terms to the left:

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


Domain of the equation: 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

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

We get rid of parentheses

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

We calculate fractions


(-16m^2)/16m^2+(-48m)/16m^2+(-4m)/16m^2-2=0

We multiply all the terms by the denominator


(-16m^2)+(-48m)+(-4m)-2*16m^2=0

Wy multiply elements

(-16m^2)-32m^2+(-48m)+(-4m)=0

We get rid of parentheses

-16m^2-32m^2-48m-4m=0

We add all the numbers together, and all the variables

-48m^2-52m=0

a = -48; b = -52; c = 0;
Δ = b2-4ac
Δ = -522-4·(-48)·0
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-52}{2*-48}=\frac{0}{-96}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+52}{2*-48}=\frac{104}{-96}
=-1+1/12
$