(n-2)Cn-4=15

Solution for (n-2)Cn-4=15 equation:

(n-2)n-4=15

We move all terms to the left:

(n-2)n-4-(15)=0

We add all the numbers together, and all the variables

(n-2)n-19=0

We multiply parentheses

n^2-2n-19=0

a = 1; b = -2; c = -19;
Δ = b2-4ac
Δ = -22-4·1·(-19)
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4\sqrt{5}}{2*1}=\frac{2-4\sqrt{5}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4\sqrt{5}}{2*1}=\frac{2+4\sqrt{5}}{2}
$