36=n-1/5n

Solution for 36=n-1/5n equation:

36=n-1/5n

We move all terms to the left:

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


Domain of the equation: 5n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

-(+n-1/5n)+36=0

We get rid of parentheses

-n+1/5n+36=0

We multiply all the terms by the denominator


-n*5n+36*5n+1=0

Wy multiply elements

-5n^2+180n+1=0

a = -5; b = 180; c = +1;
Δ = b2-4ac
Δ = 1802-4·(-5)·1
Δ = 32420
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{32420}=\sqrt{4*8105}=\sqrt{4}*\sqrt{8105}=2\sqrt{8105}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-2\sqrt{8105}}{2*-5}=\frac{-180-2\sqrt{8105}}{-10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+2\sqrt{8105}}{2*-5}=\frac{-180+2\sqrt{8105}}{-10}
$