3/12+1/6a=1/2a

Solution for 3/12+1/6a=1/2a equation:

3/12+1/6a=1/2a

We move all terms to the left:

3/12+1/6a-(1/2a)=0


Domain of the equation: 6a!=0

a!=0/6

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

1/6a-(+1/2a)+3/12=0

We get rid of parentheses

1/6a-1/2a+3/12=0

We calculate fractions


72a^2/144a^2+24a/144a^2+(-72a)/144a^2=0

We multiply all the terms by the denominator


72a^2+24a+(-72a)=0

We get rid of parentheses

72a^2+24a-72a=0

We add all the numbers together, and all the variables

72a^2-48a=0

a = 72; b = -48; c = 0;
Δ = b2-4ac
Δ = -482-4·72·0
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-48}{2*72}=\frac{0}{144}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+48}{2*72}=\frac{96}{144}
=2/3
$