5/18+1/6a=1/3a

Solution for 5/18+1/6a=1/3a equation:

5/18+1/6a=1/3a

We move all terms to the left:

5/18+1/6a-(1/3a)=0


Domain of the equation: 6a!=0

a!=0/6

a!=0

a∈R



Domain of the equation: 3a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

1/6a-(+1/3a)+5/18=0

We get rid of parentheses

1/6a-1/3a+5/18=0

We calculate fractions


270a^2/324a^2+54a/324a^2+(-108a)/324a^2=0

We multiply all the terms by the denominator


270a^2+54a+(-108a)=0

We get rid of parentheses

270a^2+54a-108a=0

We add all the numbers together, and all the variables

270a^2-54a=0

a = 270; b = -54; c = 0;
Δ = b2-4ac
Δ = -542-4·270·0
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-54}{2*270}=\frac{0}{540}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+54}{2*270}=\frac{108}{540}
=1/5
$