3/2m-4=12/m

Solution for 3/2m-4=12/m equation:

3/2m-4=12/m

We move all terms to the left:

3/2m-4-(12/m)=0


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R



Domain of the equation: m)!=0

m!=0/1

m!=0

m∈R


We add all the numbers together, and all the variables

3/2m-(+12/m)-4=0

We get rid of parentheses

3/2m-12/m-4=0

We calculate fractions


3m/2m^2+(-24m)/2m^2-4=0

We multiply all the terms by the denominator


3m+(-24m)-4*2m^2=0

Wy multiply elements

-8m^2+3m+(-24m)=0

We get rid of parentheses

-8m^2+3m-24m=0

We add all the numbers together, and all the variables

-8m^2-21m=0

a = -8; b = -21; c = 0;
Δ = b2-4ac
Δ = -212-4·(-8)·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-21}{2*-8}=\frac{0}{-16}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+21}{2*-8}=\frac{42}{-16}
=-2+5/8
$