3/8f+1/2=1/16f-3

Solution for 3/8f+1/2=1/16f-3 equation:

3/8f+1/2=1/16f-3

We move all terms to the left:

3/8f+1/2-(1/16f-3)=0


Domain of the equation: 8f!=0

f!=0/8

f!=0

f∈R



Domain of the equation: 16f-3)!=0

f∈R


We get rid of parentheses

3/8f-1/16f+3+1/2=0

We calculate fractions


128f^2/512f^2+192f/512f^2+(-32f)/512f^2+3=0

We multiply all the terms by the denominator


128f^2+192f+(-32f)+3*512f^2=0

Wy multiply elements

128f^2+1536f^2+192f+(-32f)=0

We get rid of parentheses

128f^2+1536f^2+192f-32f=0

We add all the numbers together, and all the variables

1664f^2+160f=0

a = 1664; b = 160; c = 0;
Δ = b2-4ac
Δ = 1602-4·1664·0
Δ = 25600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25600}=160$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(160)-160}{2*1664}=\frac{-320}{3328}
=-5/52
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(160)+160}{2*1664}=\frac{0}{3328}
=0
$