F(x)=-x^2+12x-24

Solution for F(x)=-x^2+12x-24 equation:

(F)=-F^2+12F-24

We move all terms to the left:

(F)-(-F^2+12F-24)=0

We get rid of parentheses

F^2-12F+F+24=0

We add all the numbers together, and all the variables

F^2-11F+24=0

a = 1; b = -11; c = +24;
Δ = b2-4ac
Δ = -112-4·1·24
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-5}{2*1}=\frac{6}{2}
=3
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+5}{2*1}=\frac{16}{2}
=8
$