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

Solution for (a+1)/5a-1/a=1 equation:

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

We move all terms to the left:

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


Domain of the equation: 5a!=0

a!=0/5

a!=0

a∈R



Domain of the equation: a!=0

a∈R


We calculate fractions


(a^2+a)/5a^2+(-5a)/5a^2-1=0

We multiply all the terms by the denominator


(a^2+a)+(-5a)-1*5a^2=0

Wy multiply elements

-5a^2+(a^2+a)+(-5a)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

-4a^2-4a=0

a = -4; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-4)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*-4}=\frac{0}{-8}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-4}=\frac{8}{-8}
=-1
$