1/3a+5=2+1/6a

Solution for 1/3a+5=2+1/6a equation:

1/3a+5=2+1/6a

We move all terms to the left:

1/3a+5-(2+1/6a)=0


Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R



Domain of the equation: 6a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

1/3a-(1/6a+2)+5=0

We get rid of parentheses

1/3a-1/6a-2+5=0

We calculate fractions


6a/18a^2+(-3a)/18a^2-2+5=0

We add all the numbers together, and all the variables

6a/18a^2+(-3a)/18a^2+3=0

We multiply all the terms by the denominator


6a+(-3a)+3*18a^2=0

Wy multiply elements

54a^2+6a+(-3a)=0

We get rid of parentheses

54a^2+6a-3a=0

We add all the numbers together, and all the variables

54a^2+3a=0

a = 54; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·54·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*54}=\frac{-6}{108}
=-1/18
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*54}=\frac{0}{108}
=0
$