F(x)=9-x^2+9-6x

Solution for F(x)=9-x^2+9-6x equation:

(F)=9-F^2+9-6F

We move all terms to the left:

(F)-(9-F^2+9-6F)=0

We get rid of parentheses

F^2+6F+F-9-9=0

We add all the numbers together, and all the variables

F^2+7F-18=0

a = 1; b = 7; c = -18;
Δ = b2-4ac
Δ = 72-4·1·(-18)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-11}{2*1}=\frac{-18}{2}
=-9
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+11}{2*1}=\frac{4}{2}
=2
$