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

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

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

We move all terms to the left:

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


Domain of the equation: 2f!=0

f!=0/2

f!=0

f∈R



Domain of the equation: 3f+2)!=0

f∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

3f/6f^2+(-4f)/6f^2+1=0

We multiply all the terms by the denominator


3f+(-4f)+1*6f^2=0

Wy multiply elements

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

We get rid of parentheses

6f^2+3f-4f=0

We add all the numbers together, and all the variables

6f^2-1f=0

a = 6; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·6·0
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*6}=\frac{0}{12}
=0
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*6}=\frac{2}{12}
=1/6
$