2a+1/3a=7/3a

Solution for 2a+1/3a=7/3a equation:

2a+1/3a=7/3a

We move all terms to the left:

2a+1/3a-(7/3a)=0


Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R



Domain of the equation: 3a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

2a+1/3a-(+7/3a)=0

We get rid of parentheses

2a+1/3a-7/3a=0

We multiply all the terms by the denominator


2a*3a+1-7=0

We add all the numbers together, and all the variables

2a*3a-6=0

Wy multiply elements

6a^2-6=0

a = 6; b = 0; c = -6;
Δ = b2-4ac
Δ = 02-4·6·(-6)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12}{2*6}=\frac{-12}{12}
=-1
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12}{2*6}=\frac{12}{12}
=1
$