F(x)=-3x^2+12x-9

Solution for F(x)=-3x^2+12x-9 equation:

(F)=-3F^2+12F-9

We move all terms to the left:

(F)-(-3F^2+12F-9)=0

We get rid of parentheses

3F^2-12F+F+9=0

We add all the numbers together, and all the variables

3F^2-11F+9=0

a = 3; b = -11; c = +9;
Δ = b2-4ac
Δ = -112-4·3·9
Δ = 13
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{-(-11)-\sqrt{13}}{2*3}=\frac{11-\sqrt{13}}{6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{13}}{2*3}=\frac{11+\sqrt{13}}{6}
$