F(x)=x2+6x+6

Solution for F(x)=x2+6x+6 equation:

(F)=F2+6F+6

We move all terms to the left:

(F)-(F2+6F+6)=0

We add all the numbers together, and all the variables

-(+F^2+6F+6)+F=0

We get rid of parentheses

-F^2-6F+F-6=0

We add all the numbers together, and all the variables

-1F^2-5F-6=0

a = -1; b = -5; c = -6;
Δ = b2-4ac
Δ = -52-4·(-1)·(-6)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-1}{2*-1}=\frac{4}{-2}
=-2
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+1}{2*-1}=\frac{6}{-2}
=-3
$