1/8f-3/4-1/4f=11

Solution for 1/8f-3/4-1/4f=11 equation:

1/8f-3/4-1/4f=11

We move all terms to the left:

1/8f-3/4-1/4f-(11)=0


Domain of the equation: 8f!=0

f!=0/8

f!=0

f∈R



Domain of the equation: 4f!=0

f!=0/4

f!=0

f∈R


determiningTheFunctionDomain
1/8f-1/4f-11-3/4=0

We calculate fractions


64f/512f^2+(-8f)/512f^2+(-24f)/512f^2-11=0

We multiply all the terms by the denominator


64f+(-8f)+(-24f)-11*512f^2=0

Wy multiply elements

-5632f^2+64f+(-8f)+(-24f)=0

We get rid of parentheses

-5632f^2+64f-8f-24f=0

We add all the numbers together, and all the variables

-5632f^2+32f=0

a = -5632; b = 32; c = 0;
Δ = b2-4ac
Δ = 322-4·(-5632)·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-32}{2*-5632}=\frac{-64}{-11264}
=1/176
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+32}{2*-5632}=\frac{0}{-11264}
=0
$