2/m-3=3/2m-1

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

2/m-3=3/2m-1

We move all terms to the left:

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


Domain of the equation: m!=0

m∈R



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

m∈R


We get rid of parentheses

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

We calculate fractions


4m/2m^2+(-3m)/2m^2+1-3=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

-4m^2+4m-3m=0

We add all the numbers together, and all the variables

-4m^2+m=0

a = -4; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-4)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-4}=\frac{-2}{-8}
=1/4
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-4}=\frac{0}{-8}
=0
$