-6(9+2f)f=9

Solution for -6(9+2f)f=9 equation:

-6(9+2f)f=9

We move all terms to the left:

-6(9+2f)f-(9)=0

We add all the numbers together, and all the variables

-6(2f+9)f-9=0

We multiply parentheses

-12f^2-54f-9=0

a = -12; b = -54; c = -9;
Δ = b2-4ac
Δ = -542-4·(-12)·(-9)
Δ = 2484
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:

$\sqrt{\Delta}=\sqrt{2484}=\sqrt{36*69}=\sqrt{36}*\sqrt{69}=6\sqrt{69}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-6\sqrt{69}}{2*-12}=\frac{54-6\sqrt{69}}{-24}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+6\sqrt{69}}{2*-12}=\frac{54+6\sqrt{69}}{-24}
$