F(x)=-x2-10x-2

Solution for F(x)=-x2-10x-2 equation:

(F)=-F2-10F-2

We move all terms to the left:

(F)-(-F2-10F-2)=0

We add all the numbers together, and all the variables

-(-1F^2-10F-2)+F=0

We get rid of parentheses

1F^2+10F+F+2=0

We add all the numbers together, and all the variables

F^2+11F+2=0

a = 1; b = 11; c = +2;
Δ = b2-4ac
Δ = 112-4·1·2
Δ = 113
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{-(11)-\sqrt{113}}{2*1}=\frac{-11-\sqrt{113}}{2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{113}}{2*1}=\frac{-11+\sqrt{113}}{2}
$