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

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

(3)=-F^2+9F

We move all terms to the left:

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

We get rid of parentheses

F^2-9F+3=0

a = 1; b = -9; c = +3;
Δ = b2-4ac
Δ = -92-4·1·3
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{-(-9)-\sqrt{69}}{2*1}=\frac{9-\sqrt{69}}{2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{69}}{2*1}=\frac{9+\sqrt{69}}{2}
$