1/15a-7/5a-1/3=1/9

Solution for 1/15a-7/5a-1/3=1/9 equation:

1/15a-7/5a-1/3=1/9

We move all terms to the left:

1/15a-7/5a-1/3-(1/9)=0


Domain of the equation: 15a!=0

a!=0/15

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

1/15a-7/5a-1/3-(+1/9)=0

We get rid of parentheses

1/15a-7/5a-1/3-1/9=0

We calculate fractions


(-3375a^2)/6075a^2+(-1125a^2)/6075a^2+405a/6075a^2+(-8505a)/6075a^2=0

We multiply all the terms by the denominator


(-3375a^2)+(-1125a^2)+405a+(-8505a)=0

We get rid of parentheses

-3375a^2-1125a^2+405a-8505a=0

We add all the numbers together, and all the variables

-4500a^2-8100a=0

a = -4500; b = -8100; c = 0;
Δ = b2-4ac
Δ = -81002-4·(-4500)·0
Δ = 65610000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{65610000}=8100$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8100)-8100}{2*-4500}=\frac{0}{-9000}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8100)+8100}{2*-4500}=\frac{16200}{-9000}
=-1+4/5
$