1/2f-2=16f

Solution for 1/2f-2=16f equation:

1/2f-2=16f

We move all terms to the left:

1/2f-2-(16f)=0


Domain of the equation: 2f!=0

f!=0/2

f!=0

f∈R


We add all the numbers together, and all the variables

-16f+1/2f-2=0

We multiply all the terms by the denominator


-16f*2f-2*2f+1=0

Wy multiply elements

-32f^2-4f+1=0

a = -32; b = -4; c = +1;
Δ = b2-4ac
Δ = -42-4·(-32)·1
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-12}{2*-32}=\frac{-8}{-64}
=1/8
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+12}{2*-32}=\frac{16}{-64}
=-1/4
$