2/3f+6=1/2f+2

Solution for 2/3f+6=1/2f+2 equation:

2/3f+6=1/2f+2

We move all terms to the left:

2/3f+6-(1/2f+2)=0


Domain of the equation: 3f!=0

f!=0/3

f!=0

f∈R



Domain of the equation: 2f+2)!=0

f∈R


We get rid of parentheses

2/3f-1/2f-2+6=0

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

24f^2+4f+(-3f)=0

We get rid of parentheses

24f^2+4f-3f=0

We add all the numbers together, and all the variables

24f^2+f=0

a = 24; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·24·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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