1/5n+5=n

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

1/5n+5=n

We move all terms to the left:

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


Domain of the equation: 5n!=0

n!=0/5

n!=0

n∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-5n^2+25n+1=0

a = -5; b = 25; c = +1;
Δ = b2-4ac
Δ = 252-4·(-5)·1
Δ = 645
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-\sqrt{645}}{2*-5}=\frac{-25-\sqrt{645}}{-10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+\sqrt{645}}{2*-5}=\frac{-25+\sqrt{645}}{-10}
$