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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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


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

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

We multiply parentheses

2F^2+4F-12F-24

We add all the numbers together, and all the variables

2F^2-8F-24

Back to the equation:

-(2F^2-8F-24)


We add all the numbers together, and all the variables

F-(2F^2-8F-24)=0

We get rid of parentheses

-2F^2+F+8F+24=0

We add all the numbers together, and all the variables

-2F^2+9F+24=0

a = -2; b = 9; c = +24;
Δ = b2-4ac
Δ = 92-4·(-2)·24
Δ = 273
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{273}}{2*-2}=\frac{-9-\sqrt{273}}{-4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{273}}{2*-2}=\frac{-9+\sqrt{273}}{-4}
$