-1/f-3/4-1/4f=11

Solution for -1/f-3/4-1/4f=11 equation:

-1/f-3/4-1/4f=11

We move all terms to the left:

-1/f-3/4-1/4f-(11)=0


Domain of the equation: f!=0

f∈R



Domain of the equation: 4f!=0

f!=0/4

f!=0

f∈R


determiningTheFunctionDomain
-1/f-1/4f-11-3/4=0

We calculate fractions


(-64f)/64f^2+(-f)/64f^2+(-3f)/64f^2-11=0

We add all the numbers together, and all the variables

(-64f)/64f^2+(-1f)/64f^2+(-3f)/64f^2-11=0

We multiply all the terms by the denominator


(-64f)+(-1f)+(-3f)-11*64f^2=0

Wy multiply elements

-704f^2+(-64f)+(-1f)+(-3f)=0

We get rid of parentheses

-704f^2-64f-1f-3f=0

We add all the numbers together, and all the variables

-704f^2-68f=0

a = -704; b = -68; c = 0;
Δ = b2-4ac
Δ = -682-4·(-704)·0
Δ = 4624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4624}=68$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-68)-68}{2*-704}=\frac{0}{-1408}
=0
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-68)+68}{2*-704}=\frac{136}{-1408}
=-17/176
$