F(x)=-0.67(x+2)(x-3)

Solution for F(x)=-0.67(x+2)(x-3) equation:

(F)=-0.67(F+2)(F-3)

We move all terms to the left:

(F)-(-0.67(F+2)(F-3))=0

We multiply parentheses ..

-(-0.67(+F^2-3F+2F-6))+F=0


We calculate terms in parentheses: -(-0.67(+F^2-3F+2F-6)), so:

-0.67(+F^2-3F+2F-6)

We multiply parentheses

-0.67F^2+2.01F-1.34F+4.02

We add all the numbers together, and all the variables

-0.67F^2+0.67F+4.02

Back to the equation:

-(-0.67F^2+0.67F+4.02)


We get rid of parentheses

0.67F^2-0.67F+F-4.02=0

We add all the numbers together, and all the variables

0.67F^2+0.33F-4.02=0

a = 0.67; b = 0.33; c = -4.02;
Δ = b2-4ac
Δ = 0.332-4·0.67·(-4.02)
Δ = 10.8825
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{-(0.33)-\sqrt{10.8825}}{2*0.67}=\frac{-0.33-\sqrt{10.8825}}{1.34}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.33)+\sqrt{10.8825}}{2*0.67}=\frac{-0.33+\sqrt{10.8825}}{1.34}
$