3/2m+2=1/6m-3

Solution for 3/2m+2=1/6m-3 equation:

3/2m+2=1/6m-3

We move all terms to the left:

3/2m+2-(1/6m-3)=0


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R



Domain of the equation: 6m-3)!=0

m∈R


We get rid of parentheses

3/2m-1/6m+3+2=0

We calculate fractions


18m/12m^2+(-2m)/12m^2+3+2=0

We add all the numbers together, and all the variables

18m/12m^2+(-2m)/12m^2+5=0

We multiply all the terms by the denominator


18m+(-2m)+5*12m^2=0

Wy multiply elements

60m^2+18m+(-2m)=0

We get rid of parentheses

60m^2+18m-2m=0

We add all the numbers together, and all the variables

60m^2+16m=0

a = 60; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·60·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*60}=\frac{-32}{120}
=-4/15
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*60}=\frac{0}{120}
=0
$