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

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

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

We move all terms to the left:

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


Domain of the equation: 4m!=0

m!=0/4

m!=0

m∈R



Domain of the equation: 2m+12)!=0

m∈R


We get rid of parentheses

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

We calculate fractions


6m/128m^2+(-192m)/128m^2+(-4m)/128m^2-12=0

We multiply all the terms by the denominator


6m+(-192m)+(-4m)-12*128m^2=0

Wy multiply elements

-1536m^2+6m+(-192m)+(-4m)=0

We get rid of parentheses

-1536m^2+6m-192m-4m=0

We add all the numbers together, and all the variables

-1536m^2-190m=0

a = -1536; b = -190; c = 0;
Δ = b2-4ac
Δ = -1902-4·(-1536)·0
Δ = 36100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36100}=190$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-190)-190}{2*-1536}=\frac{0}{-3072}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-190)+190}{2*-1536}=\frac{380}{-3072}
=-95/768
$