F=9-6x(-3+x)

Solution for F=9-6x(-3+x) equation:

=9-6F(-3+F)

We move all terms to the left:

-(9-6F(-3+F))=0

We add all the numbers together, and all the variables

-(9-6F(F-3))=0


We calculate terms in parentheses: -(9-6F(F-3)), so:

9-6F(F-3)

determiningTheFunctionDomain
-6F(F-3)+9

We multiply parentheses

-6F^2+18F+9

Back to the equation:

-(-6F^2+18F+9)


We get rid of parentheses

6F^2-18F-9=0

a = 6; b = -18; c = -9;
Δ = b2-4ac
Δ = -182-4·6·(-9)
Δ = 540
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{540}=\sqrt{36*15}=\sqrt{36}*\sqrt{15}=6\sqrt{15}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{15}}{2*6}=\frac{18-6\sqrt{15}}{12}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{15}}{2*6}=\frac{18+6\sqrt{15}}{12}
$