1/3f+21=1/2f+18

Solution for 1/3f+21=1/2f+18 equation:

1/3f+21=1/2f+18

We move all terms to the left:

1/3f+21-(1/2f+18)=0


Domain of the equation: 3f!=0

f!=0/3

f!=0

f∈R



Domain of the equation: 2f+18)!=0

f∈R


We get rid of parentheses

1/3f-1/2f-18+21=0

We calculate fractions


2f/6f^2+(-3f)/6f^2-18+21=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

18f^2+2f+(-3f)=0

We get rid of parentheses

18f^2+2f-3f=0

We add all the numbers together, and all the variables

18f^2-1f=0

a = 18; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·18·0
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*18}=\frac{0}{36}
=0
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*18}=\frac{2}{36}
=1/18
$