13/15+1/5a=1/3a

Solution for 13/15+1/5a=1/3a equation:

13/15+1/5a=1/3a

We move all terms to the left:

13/15+1/5a-(1/3a)=0


Domain of the equation: 5a!=0

a!=0/5

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

1/5a-(+1/3a)+13/15=0

We get rid of parentheses

1/5a-1/3a+13/15=0

We calculate fractions


585a^2/225a^2+45a/225a^2+(-75a)/225a^2=0

We multiply all the terms by the denominator


585a^2+45a+(-75a)=0

We get rid of parentheses

585a^2+45a-75a=0

We add all the numbers together, and all the variables

585a^2-30a=0

a = 585; b = -30; c = 0;
Δ = b2-4ac
Δ = -302-4·585·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-30}{2*585}=\frac{0}{1170}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+30}{2*585}=\frac{60}{1170}
=2/39
$