F(n)=n^2-2n-15

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

(F)=F^2-2F-15

We move all terms to the left:

(F)-(F^2-2F-15)=0

We get rid of parentheses

-F^2+F+2F+15=0

We add all the numbers together, and all the variables

-1F^2+3F+15=0

a = -1; b = 3; c = +15;
Δ = b2-4ac
Δ = 32-4·(-1)·15
Δ = 69
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{69}}{2*-1}=\frac{-3-\sqrt{69}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{69}}{2*-1}=\frac{-3+\sqrt{69}}{-2}
$