2/3a-1/6a=3

Solution for 2/3a-1/6a=3 equation:

2/3a-1/6a=3

We move all terms to the left:

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


Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R



Domain of the equation: 6a!=0

a!=0/6

a!=0

a∈R


We calculate fractions


12a/18a^2+(-3a)/18a^2-3=0

We multiply all the terms by the denominator


12a+(-3a)-3*18a^2=0

Wy multiply elements

-54a^2+12a+(-3a)=0

We get rid of parentheses

-54a^2+12a-3a=0

We add all the numbers together, and all the variables

-54a^2+9a=0

a = -54; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-54)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-54}=\frac{-18}{-108}
=1/6
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-54}=\frac{0}{-108}
=0
$