F(x)=-x2-7x-5

Solution for F(x)=-x2-7x-5 equation:

(F)=-F2-7F-5

We move all terms to the left:

(F)-(-F2-7F-5)=0

We add all the numbers together, and all the variables

-(-1F^2-7F-5)+F=0

We get rid of parentheses

1F^2+7F+F+5=0

We add all the numbers together, and all the variables

F^2+8F+5=0

a = 1; b = 8; c = +5;
Δ = b2-4ac
Δ = 82-4·1·5
Δ = 44
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:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{11}}{2*1}=\frac{-8-2\sqrt{11}}{2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{11}}{2*1}=\frac{-8+2\sqrt{11}}{2}
$