-4(3+f)6f=-24

Solution for -4(3+f)6f=-24 equation:

-4(3+f)6f=-24

We move all terms to the left:

-4(3+f)6f-(-24)=0

We add all the numbers together, and all the variables

-4(f+3)6f-(-24)=0

We add all the numbers together, and all the variables

-4(f+3)6f+24=0

We multiply parentheses

-24f^2-72f+24=0

a = -24; b = -72; c = +24;
Δ = b2-4ac
Δ = -722-4·(-24)·24
Δ = 7488
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:

$\sqrt{\Delta}=\sqrt{7488}=\sqrt{576*13}=\sqrt{576}*\sqrt{13}=24\sqrt{13}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-24\sqrt{13}}{2*-24}=\frac{72-24\sqrt{13}}{-48}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+24\sqrt{13}}{2*-24}=\frac{72+24\sqrt{13}}{-48}
$