3f=1/9f=

Solution for 3f=1/9f= equation:

3f=1/9f=

We move all terms to the left:

3f-(1/9f)=0


Domain of the equation: 9f)!=0

f!=0/1

f!=0

f∈R


We add all the numbers together, and all the variables

3f-(+1/9f)=0

We get rid of parentheses

3f-1/9f=0

We multiply all the terms by the denominator


3f*9f-1=0

Wy multiply elements

27f^2-1=0

a = 27; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·27·(-1)
Δ = 108
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:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{3}}{2*27}=\frac{0-6\sqrt{3}}{54}
=-\frac{6\sqrt{3}}{54}
=-\frac{\sqrt{3}}{9}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{3}}{2*27}=\frac{0+6\sqrt{3}}{54}
=\frac{6\sqrt{3}}{54}
=\frac{\sqrt{3}}{9}
$