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+9F-12=0

a = -1; b = 9; c = -12;
Δ = b2-4ac
Δ = 92-4·(-1)·(-12)
Δ = 33
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{-(9)-\sqrt{33}}{2*-1}=\frac{-9-\sqrt{33}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{33}}{2*-1}=\frac{-9+\sqrt{33}}{-2}
$