F(x)=-x^2-7x-8

Solution for F(x)=-x^2-7x-8 equation:

(F)=-F^2-7F-8

We move all terms to the left:

(F)-(-F^2-7F-8)=0

We get rid of parentheses

F^2+7F+F+8=0

We add all the numbers together, and all the variables

F^2+8F+8=0

a = 1; b = 8; c = +8;
Δ = b2-4ac
Δ = 82-4·1·8
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{2}}{2*1}=\frac{-8-4\sqrt{2}}{2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{2}}{2*1}=\frac{-8+4\sqrt{2}}{2}
$