3/2m-16+m+2/4m-32=m-8/4m

Solution for 3/2m-16+m+2/4m-32=m-8/4m equation:

3/2m-16+m+2/4m-32=m-8/4m

We move all terms to the left:

3/2m-16+m+2/4m-32-(m-8/4m)=0


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R



Domain of the equation: 4m!=0

m!=0/4

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

3/2m+m+2/4m-(+m-8/4m)-16-32=0

We add all the numbers together, and all the variables

m+3/2m+2/4m-(+m-8/4m)-48=0

We get rid of parentheses

m+3/2m+2/4m-m+8/4m-48=0

We calculate fractions


m-m+12m/8m^2+(16m+2)/8m^2-48=0

We add all the numbers together, and all the variables

12m/8m^2+(16m+2)/8m^2-48=0

We multiply all the terms by the denominator


12m+(16m+2)-48*8m^2=0

Wy multiply elements

-384m^2+12m+(16m+2)=0

We get rid of parentheses

-384m^2+12m+16m+2=0

We add all the numbers together, and all the variables

-384m^2+28m+2=0

a = -384; b = 28; c = +2;
Δ = b2-4ac
Δ = 282-4·(-384)·2
Δ = 3856
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:

$\sqrt{\Delta}=\sqrt{3856}=\sqrt{16*241}=\sqrt{16}*\sqrt{241}=4\sqrt{241}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-4\sqrt{241}}{2*-384}=\frac{-28-4\sqrt{241}}{-768}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+4\sqrt{241}}{2*-384}=\frac{-28+4\sqrt{241}}{-768}
$