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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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


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

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

We get rid of parentheses

-F^2+2F-6F+12

We add all the numbers together, and all the variables

-1F^2-4F+12

Back to the equation:

-(-1F^2-4F+12)


We get rid of parentheses

1F^2+4F+F-12=0

We add all the numbers together, and all the variables

F^2+5F-12=0

a = 1; b = 5; c = -12;
Δ = b2-4ac
Δ = 52-4·1·(-12)
Δ = 73
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{-(5)-\sqrt{73}}{2*1}=\frac{-5-\sqrt{73}}{2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{73}}{2*1}=\frac{-5+\sqrt{73}}{2}
$