F(-2)=-x^2-9x

Solution for F(-2)=-x^2-9x equation:

(-2)=-F^2-9F

We move all terms to the left:

(-2)-(-F^2-9F)=0

We add all the numbers together, and all the variables

-(-F^2-9F)-2=0

We get rid of parentheses

F^2+9F-2=0

a = 1; b = 9; c = -2;
Δ = b2-4ac
Δ = 92-4·1·(-2)
Δ = 89
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{-(9)-\sqrt{89}}{2*1}=\frac{-9-\sqrt{89}}{2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{89}}{2*1}=\frac{-9+\sqrt{89}}{2}
$