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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -1; b = -1; c = +24;
Δ = b2-4ac
Δ = -12-4·(-1)·24
Δ = 97
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{-(-1)-\sqrt{97}}{2*-1}=\frac{1-\sqrt{97}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{97}}{2*-1}=\frac{1+\sqrt{97}}{-2}
$