F(x)=(x+2)(x+6)

Solution for F(x)=(x+2)(x+6) equation:

(F)=(F+2)(F+6)

We move all terms to the left:

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

We multiply parentheses ..

-((+F^2+6F+2F+12))+F=0


We calculate terms in parentheses: -((+F^2+6F+2F+12)), so:

(+F^2+6F+2F+12)

We get rid of parentheses

F^2+6F+2F+12

We add all the numbers together, and all the variables

F^2+8F+12

Back to the equation:

-(F^2+8F+12)


We add all the numbers together, and all the variables

F-(F^2+8F+12)=0

We get rid of parentheses

-F^2+F-8F-12=0

We add all the numbers together, and all the variables

-1F^2-7F-12=0

a = -1; b = -7; c = -12;
Δ = b2-4ac
Δ = -72-4·(-1)·(-12)
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{-(-7)-1}{2*-1}=\frac{6}{-2}
=-3
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+1}{2*-1}=\frac{8}{-2}
=-4
$