3/3f+4=2/f-4

Solution for 3/3f+4=2/f-4 equation:

3/3f+4=2/f-4

We move all terms to the left:

3/3f+4-(2/f-4)=0


Domain of the equation: 3f!=0

f!=0/3

f!=0

f∈R



Domain of the equation: f-4)!=0

f∈R


We get rid of parentheses

3/3f-2/f+4+4=0

We calculate fractions


3f/3f^2+(-6f)/3f^2+4+4=0

We add all the numbers together, and all the variables

3f/3f^2+(-6f)/3f^2+8=0

We multiply all the terms by the denominator


3f+(-6f)+8*3f^2=0

Wy multiply elements

24f^2+3f+(-6f)=0

We get rid of parentheses

24f^2+3f-6f=0

We add all the numbers together, and all the variables

24f^2-3f=0

a = 24; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·24·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*24}=\frac{0}{48}
=0
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*24}=\frac{6}{48}
=1/8
$