A+1/5a-1/a=1

Solution for A+1/5a-1/a=1 equation:

+1/5A-1/A=1

We move all terms to the left:

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

-5A^2+A-5A=0

We add all the numbers together, and all the variables

-5A^2-4A=0

a = -5; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-5)·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*-5}=\frac{0}{-10}
=0
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-5}=\frac{8}{-10}
=-4/5
$