5/9a+1/3=5/6a

Solution for 5/9a+1/3=5/6a equation:

5/9a+1/3=5/6a

We move all terms to the left:

5/9a+1/3-(5/6a)=0


Domain of the equation: 9a!=0

a!=0/9

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

5/9a-(+5/6a)+1/3=0

We get rid of parentheses

5/9a-5/6a+1/3=0

We calculate fractions


324a^2/486a^2+270a/486a^2+(-405a)/486a^2=0

We multiply all the terms by the denominator


324a^2+270a+(-405a)=0

We get rid of parentheses

324a^2+270a-405a=0

We add all the numbers together, and all the variables

324a^2-135a=0

a = 324; b = -135; c = 0;
Δ = b2-4ac
Δ = -1352-4·324·0
Δ = 18225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{18225}=135$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-135)-135}{2*324}=\frac{0}{648}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-135)+135}{2*324}=\frac{270}{648}
=5/12
$