2a/a^2=1/3

Solution for 2a/a^2=1/3 equation:

2a/a^2=1/3

We move all terms to the left:

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


Domain of the equation: a^2!=0

a^2!=0/

a^2!=√0

a!=0

a∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


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

We get rid of parentheses

-1a^2+6a=0

a = -1; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-1)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-1}=\frac{-12}{-2}
=+6
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-1}=\frac{0}{-2}
=0
$