20/n=n-1

Solution for 20/n=n-1 equation:

20/n=n-1

We move all terms to the left:

20/n-(n-1)=0


Domain of the equation: n!=0

n∈R


We get rid of parentheses

20/n-n+1=0

We multiply all the terms by the denominator


-n*n+1*n+20=0

We add all the numbers together, and all the variables

n-n*n+20=0

Wy multiply elements

-1n^2+n+20=0

a = -1; b = 1; c = +20;
Δ = b2-4ac
Δ = 12-4·(-1)·20
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-9}{2*-1}=\frac{-10}{-2}
=+5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+9}{2*-1}=\frac{8}{-2}
=-4
$