5/3m-3=2/2m-1

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

5/3m-3=2/2m-1

We move all terms to the left:

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


Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R



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

m∈R


We get rid of parentheses

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

We calculate fractions


10m/6m^2+(-6m)/6m^2+1-3=0

We add all the numbers together, and all the variables

10m/6m^2+(-6m)/6m^2-2=0

We multiply all the terms by the denominator


10m+(-6m)-2*6m^2=0

Wy multiply elements

-12m^2+10m+(-6m)=0

We get rid of parentheses

-12m^2+10m-6m=0

We add all the numbers together, and all the variables

-12m^2+4m=0

a = -12; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-12)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-12}=\frac{-8}{-24}
=1/3
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-12}=\frac{0}{-24}
=0
$