1/2a=1/6a+3

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

1/2a=1/6a+3

We move all terms to the left:

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


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R



Domain of the equation: 6a+3)!=0

a∈R


We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


6a+(-2a)-3*12a^2=0

Wy multiply elements

-36a^2+6a+(-2a)=0

We get rid of parentheses

-36a^2+6a-2a=0

We add all the numbers together, and all the variables

-36a^2+4a=0

a = -36; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-36)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-36}=\frac{-8}{-72}
=1/9
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-36}=\frac{0}{-72}
=0
$