1/3f=f

Solution for 1/3f=f equation:

1/3f=f

We move all terms to the left:

1/3f-(f)=0


Domain of the equation: 3f!=0

f!=0/3

f!=0

f∈R


We add all the numbers together, and all the variables

-1f+1/3f=0

We multiply all the terms by the denominator


-1f*3f+1=0

Wy multiply elements

-3f^2+1=0

a = -3; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-3)·1
Δ = 12
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:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{3}}{2*-3}=\frac{0-2\sqrt{3}}{-6}
=-\frac{2\sqrt{3}}{-6}
=-\frac{\sqrt{3}}{-3}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{3}}{2*-3}=\frac{0+2\sqrt{3}}{-6}
=\frac{2\sqrt{3}}{-6}
=\frac{\sqrt{3}}{-3}
$