F(x)=24-5x-x2

Solution for F(x)=24-5x-x2 equation:

(F)=24-5F-F2

We move all terms to the left:

(F)-(24-5F-F2)=0

We add all the numbers together, and all the variables

-(-5F-1F^2+24)+F=0

We get rid of parentheses

1F^2+5F+F-24=0

We add all the numbers together, and all the variables

F^2+6F-24=0

a = 1; b = 6; c = -24;
Δ = b2-4ac
Δ = 62-4·1·(-24)
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{33}}{2*1}=\frac{-6-2\sqrt{33}}{2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{33}}{2*1}=\frac{-6+2\sqrt{33}}{2}
$