F=x^2+22x+24

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

=F^2+22F+24

We move all terms to the left:

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

We get rid of parentheses

-F^2-22F-24=0

We add all the numbers together, and all the variables

-1F^2-22F-24=0

a = -1; b = -22; c = -24;
Δ = b2-4ac
Δ = -222-4·(-1)·(-24)
Δ = 388
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:

$\sqrt{\Delta}=\sqrt{388}=\sqrt{4*97}=\sqrt{4}*\sqrt{97}=2\sqrt{97}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{97}}{2*-1}=\frac{22-2\sqrt{97}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{97}}{2*-1}=\frac{22+2\sqrt{97}}{-2}
$