(n^2-2n-15)/n-2=0

Solution for (n^2-2n-15)/n-2=0 equation:

(n^2-2n-15)/n-2=0


Domain of the equation: n!=0

n∈R


We multiply all the terms by the denominator


(n^2-2n-15)-2*n=0

We add all the numbers together, and all the variables

-2n+(n^2-2n-15)=0

We get rid of parentheses

n^2-2n-2n-15=0

We add all the numbers together, and all the variables

n^2-4n-15=0

a = 1; b = -4; c = -15;
Δ = b2-4ac
Δ = -42-4·1·(-15)
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{19}}{2*1}=\frac{4-2\sqrt{19}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{19}}{2*1}=\frac{4+2\sqrt{19}}{2}
$