n*5/(n-12)=n

Solution for n*5/(n-12)=n equation:

n*5/(n-12)=n

We move all terms to the left:

n*5/(n-12)-(n)=0


Domain of the equation: (n-12)!=0

We move all terms containing n to the left, all other terms to the right

n!=12

n∈R


We add all the numbers together, and all the variables

-1n+n*5/(n-12)=0

We multiply all the terms by the denominator


-1n*(n-12)+n*5=0

We multiply parentheses

-n^2+12n+n*5=0

Wy multiply elements

-n^2+12n+5n=0

We add all the numbers together, and all the variables

-1n^2+17n=0

a = -1; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·(-1)·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*-1}=\frac{-34}{-2}
=+17
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*-1}=\frac{0}{-2}
=0
$