N/(n-1)=2n-24

Solution for N/(n-1)=2n-24 equation:

/(N-1)=2N-24

We move all terms to the left:

/(N-1)-(2N-24)=0


Domain of the equation: (N-1)!=0

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

N!=1

N∈R


We get rid of parentheses

/(N-1)-2N+24=0

We multiply all the terms by the denominator


-2N*(N-1)+24*(N-1)+=0

We add all the numbers together, and all the variables

-2N*(N-1)+24*(N-1)=0

We multiply parentheses

-2N^2+2N+24N-24=0

We add all the numbers together, and all the variables

-2N^2+26N-24=0

a = -2; b = 26; c = -24;
Δ = b2-4ac
Δ = 262-4·(-2)·(-24)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$N_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$N_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$N_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-22}{2*-2}=\frac{-48}{-4}
=+12
$
$N_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+22}{2*-2}=\frac{-4}{-4}
=1
$