2/3a-1/6=1/2a

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

2/3a-1/6=1/2a

We move all terms to the left:

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


Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R



Domain of the equation: 2a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-12a^2)/216a^2+144a/216a^2+(-108a)/216a^2=0

We multiply all the terms by the denominator


(-12a^2)+144a+(-108a)=0

We get rid of parentheses

-12a^2+144a-108a=0

We add all the numbers together, and all the variables

-12a^2+36a=0

a = -12; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·(-12)·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-36}{2*-12}=\frac{-72}{-24}
=+3
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*-12}=\frac{0}{-24}
=0
$