3/4f-4=1/2f+1

Solution for 3/4f-4=1/2f+1 equation:

3/4f-4=1/2f+1

We move all terms to the left:

3/4f-4-(1/2f+1)=0


Domain of the equation: 4f!=0

f!=0/4

f!=0

f∈R



Domain of the equation: 2f+1)!=0

f∈R


We get rid of parentheses

3/4f-1/2f-1-4=0

We calculate fractions


6f/8f^2+(-4f)/8f^2-1-4=0

We add all the numbers together, and all the variables

6f/8f^2+(-4f)/8f^2-5=0

We multiply all the terms by the denominator


6f+(-4f)-5*8f^2=0

Wy multiply elements

-40f^2+6f+(-4f)=0

We get rid of parentheses

-40f^2+6f-4f=0

We add all the numbers together, and all the variables

-40f^2+2f=0

a = -40; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-40)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-40}=\frac{-4}{-80}
=1/20
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-40}=\frac{0}{-80}
=0
$