1/a+1/5a=3

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

1/a+1/5a=3

We move all terms to the left:

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


Domain of the equation: a!=0

a∈R



Domain of the equation: 5a!=0

a!=0/5

a!=0

a∈R


We calculate fractions


5a/5a^2+a/5a^2-3=0

We multiply all the terms by the denominator


5a+a-3*5a^2=0

We add all the numbers together, and all the variables

6a-3*5a^2=0

Wy multiply elements

-15a^2+6a=0

a = -15; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-15)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-15}=\frac{-12}{-30}
=2/5
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-15}=\frac{0}{-30}
=0
$