F(x)=-3x^2+27

Solution for F(x)=-3x^2+27 equation:

(F)=-3F^2+27

We move all terms to the left:

(F)-(-3F^2+27)=0

We get rid of parentheses

3F^2+F-27=0

a = 3; b = 1; c = -27;
Δ = b2-4ac
Δ = 12-4·3·(-27)
Δ = 325
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:

$\sqrt{\Delta}=\sqrt{325}=\sqrt{25*13}=\sqrt{25}*\sqrt{13}=5\sqrt{13}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-5\sqrt{13}}{2*3}=\frac{-1-5\sqrt{13}}{6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+5\sqrt{13}}{2*3}=\frac{-1+5\sqrt{13}}{6}
$