F(x)=-x^2-12x-39

Solution for F(x)=-x^2-12x-39 equation:

(F)=-F^2-12F-39

We move all terms to the left:

(F)-(-F^2-12F-39)=0

We get rid of parentheses

F^2+12F+F+39=0

We add all the numbers together, and all the variables

F^2+13F+39=0

a = 1; b = 13; c = +39;
Δ = b2-4ac
Δ = 132-4·1·39
Δ = 13
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{-(13)-\sqrt{13}}{2*1}=\frac{-13-\sqrt{13}}{2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{13}}{2*1}=\frac{-13+\sqrt{13}}{2}
$