2/3f-3/7-1/7f=3

Solution for 2/3f-3/7-1/7f=3 equation:

2/3f-3/7-1/7f=3

We move all terms to the left:

2/3f-3/7-1/7f-(3)=0


Domain of the equation: 3f!=0

f!=0/3

f!=0

f∈R



Domain of the equation: 7f!=0

f!=0/7

f!=0

f∈R


determiningTheFunctionDomain
2/3f-1/7f-3-3/7=0

We calculate fractions


686f/1029f^2+(-3f)/1029f^2+(-9f)/1029f^2-3=0

We multiply all the terms by the denominator


686f+(-3f)+(-9f)-3*1029f^2=0

Wy multiply elements

-3087f^2+686f+(-3f)+(-9f)=0

We get rid of parentheses

-3087f^2+686f-3f-9f=0

We add all the numbers together, and all the variables

-3087f^2+674f=0

a = -3087; b = 674; c = 0;
Δ = b2-4ac
Δ = 6742-4·(-3087)·0
Δ = 454276
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{454276}=674$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(674)-674}{2*-3087}=\frac{-1348}{-6174}
=674/3087
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(674)+674}{2*-3087}=\frac{0}{-6174}
=0
$