1/2f-1=1/6f

Solution for 1/2f-1=1/6f equation:

1/2f-1=1/6f

We move all terms to the left:

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


Domain of the equation: 2f!=0

f!=0/2

f!=0

f∈R



Domain of the equation: 6f)!=0

f!=0/1

f!=0

f∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


6f/12f^2+(-2f)/12f^2-1=0

We multiply all the terms by the denominator


6f+(-2f)-1*12f^2=0

Wy multiply elements

-12f^2+6f+(-2f)=0

We get rid of parentheses

-12f^2+6f-2f=0

We add all the numbers together, and all the variables

-12f^2+4f=0

a = -12; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-12)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-12}=\frac{-8}{-24}
=1/3
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-12}=\frac{0}{-24}
=0
$