F(n)=-n^2-6n-5

Solution for F(n)=-n^2-6n-5 equation:

(F)=-F^2-6F-5

We move all terms to the left:

(F)-(-F^2-6F-5)=0

We get rid of parentheses

F^2+6F+F+5=0

We add all the numbers together, and all the variables

F^2+7F+5=0

a = 1; b = 7; c = +5;
Δ = b2-4ac
Δ = 72-4·1·5
Δ = 29
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{-(7)-\sqrt{29}}{2*1}=\frac{-7-\sqrt{29}}{2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{29}}{2*1}=\frac{-7+\sqrt{29}}{2}
$