1/6f+2/3f=1

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

1/6f+2/3f=1

We move all terms to the left:

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


Domain of the equation: 6f!=0

f!=0/6

f!=0

f∈R



Domain of the equation: 3f!=0

f!=0/3

f!=0

f∈R


We calculate fractions


3f/18f^2+12f/18f^2-1=0

We multiply all the terms by the denominator


3f+12f-1*18f^2=0

We add all the numbers together, and all the variables

15f-1*18f^2=0

Wy multiply elements

-18f^2+15f=0

a = -18; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·(-18)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*-18}=\frac{-30}{-36}
=5/6
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*-18}=\frac{0}{-36}
=0
$