/5n+1=n-1

Solution for /5n+1=n-1 equation:

/5n+1=n-1

We move all terms to the left:

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


Domain of the equation: 5n!=0

n!=0/5

n!=0

n∈R


We get rid of parentheses

/5n-n+1+1=0

We multiply all the terms by the denominator


-n*5n+1*5n+1*5n+=0

We add all the numbers together, and all the variables

-n*5n+1*5n+1*5n=0

Wy multiply elements

-5n^2+5n+5n=0

We add all the numbers together, and all the variables

-5n^2+10n=0

a = -5; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-5)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-5}=\frac{-20}{-10}
=+2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-5}=\frac{0}{-10}
=0
$