1/3a+1/5a=14/15

Solution for 1/3a+1/5a=14/15 equation:

1/3a+1/5a=14/15

We move all terms to the left:

1/3a+1/5a-(14/15)=0


Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R



Domain of the equation: 5a!=0

a!=0/5

a!=0

a∈R


We add all the numbers together, and all the variables

1/3a+1/5a-(+14/15)=0

We get rid of parentheses

1/3a+1/5a-14/15=0

We calculate fractions


(-1050a^2)/225a^2+75a/225a^2+45a/225a^2=0

We multiply all the terms by the denominator


(-1050a^2)+75a+45a=0

We add all the numbers together, and all the variables

(-1050a^2)+120a=0

We get rid of parentheses

-1050a^2+120a=0

a = -1050; b = 120; c = 0;
Δ = b2-4ac
Δ = 1202-4·(-1050)·0
Δ = 14400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14400}=120$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-120}{2*-1050}=\frac{-240}{-2100}
=4/35
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+120}{2*-1050}=\frac{0}{-2100}
=0
$