1/2f+1=4f

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

1/2f+1=4f

We move all terms to the left:

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


Domain of the equation: 2f!=0

f!=0/2

f!=0

f∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


-4f*2f+1*2f+1=0

Wy multiply elements

-8f^2+2f+1=0

a = -8; b = 2; c = +1;
Δ = b2-4ac
Δ = 22-4·(-8)·1
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-6}{2*-8}=\frac{-8}{-16}
=1/2
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+6}{2*-8}=\frac{4}{-16}
=-1/4
$