2/a+3=3/3a-1

Solution for 2/a+3=3/3a-1 equation:

2/a+3=3/3a-1

We move all terms to the left:

2/a+3-(3/3a-1)=0


Domain of the equation: a!=0

a∈R



Domain of the equation: 3a-1)!=0

a∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

6a/3a^2+(-3a)/3a^2+4=0

We multiply all the terms by the denominator


6a+(-3a)+4*3a^2=0

Wy multiply elements

12a^2+6a+(-3a)=0

We get rid of parentheses

12a^2+6a-3a=0

We add all the numbers together, and all the variables

12a^2+3a=0

a = 12; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·12·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*12}=\frac{-6}{24}
=-1/4
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*12}=\frac{0}{24}
=0
$