F(x)=-3x^2+18x-24

Solution for F(x)=-3x^2+18x-24 equation:

(F)=-3F^2+18F-24

We move all terms to the left:

(F)-(-3F^2+18F-24)=0

We get rid of parentheses

3F^2-18F+F+24=0

We add all the numbers together, and all the variables

3F^2-17F+24=0

a = 3; b = -17; c = +24;
Δ = b2-4ac
Δ = -172-4·3·24
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-1}{2*3}=\frac{16}{6}
=2+2/3
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+1}{2*3}=\frac{18}{6}
=3
$