2(3/2m+1)=3(5/3m-2)

Solution for 2(3/2m+1)=3(5/3m-2) equation:

2(3/2m+1)=3(5/3m-2)

We move all terms to the left:

2(3/2m+1)-(3(5/3m-2))=0


Domain of the equation: 2m+1)!=0

m∈R



Domain of the equation: 3m-2))!=0

m∈R


We multiply parentheses

6m-(3(5/3m-2))+2=0

We multiply all the terms by the denominator


6m*3m+2*3m-2))-(3(5-2))=0

We add all the numbers together, and all the variables

6m*3m+2*3m-2))-(33)=0

We add all the numbers together, and all the variables

6m*3m+2*3m=0

Wy multiply elements

18m^2+6m=0

a = 18; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·18·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*18}=\frac{-12}{36}
=-1/3
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*18}=\frac{0}{36}
=0
$