4/3m+1=6/2m-1

Solution for 4/3m+1=6/2m-1 equation:

4/3m+1=6/2m-1

We move all terms to the left:

4/3m+1-(6/2m-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

4/3m-6/2m+1+1=0

We calculate fractions


8m/6m^2+(-18m)/6m^2+1+1=0

We add all the numbers together, and all the variables

8m/6m^2+(-18m)/6m^2+2=0

We multiply all the terms by the denominator


8m+(-18m)+2*6m^2=0

Wy multiply elements

12m^2+8m+(-18m)=0

We get rid of parentheses

12m^2+8m-18m=0

We add all the numbers together, and all the variables

12m^2-10m=0

a = 12; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·12·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*12}=\frac{0}{24}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*12}=\frac{20}{24}
=5/6
$