F(x)=24+x^2+22x

Solution for F(x)=24+x^2+22x equation:

(F)=24+F^2+22F

We move all terms to the left:

(F)-(24+F^2+22F)=0

We get rid of parentheses

-F^2-22F+F-24=0

We add all the numbers together, and all the variables

-1F^2-21F-24=0

a = -1; b = -21; c = -24;
Δ = b2-4ac
Δ = -212-4·(-1)·(-24)
Δ = 345
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{-(-21)-\sqrt{345}}{2*-1}=\frac{21-\sqrt{345}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{345}}{2*-1}=\frac{21+\sqrt{345}}{-2}
$