F(x)=-x^2+24+180

Solution for F(x)=-x^2+24+180 equation:

(F)=-F^2+24+180

We move all terms to the left:

(F)-(-F^2+24+180)=0

We get rid of parentheses

F^2+F-24-180=0

We add all the numbers together, and all the variables

F^2+F-204=0

a = 1; b = 1; c = -204;
Δ = b2-4ac
Δ = 12-4·1·(-204)
Δ = 817
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{817}}{2*1}=\frac{-1-\sqrt{817}}{2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{817}}{2*1}=\frac{-1+\sqrt{817}}{2}
$