F(-x)=x^2-3x-9

Solution for F(-x)=x^2-3x-9 equation:

(-F)=F^2-3F-9

We move all terms to the left:

(-F)-(F^2-3F-9)=0

We add all the numbers together, and all the variables

(-1F)-(F^2-3F-9)=0

We get rid of parentheses

-F^2-1F+3F+9=0

We add all the numbers together, and all the variables

-1F^2+2F+9=0

a = -1; b = 2; c = +9;
Δ = b2-4ac
Δ = 22-4·(-1)·9
Δ = 40
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{10}}{2*-1}=\frac{-2-2\sqrt{10}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{10}}{2*-1}=\frac{-2+2\sqrt{10}}{-2}
$