3/16y=1/y+3

Solution for 3/16y=1/y+3 equation:

3/16y=1/y+3

We move all terms to the left:

3/16y-(1/y+3)=0


Domain of the equation: 16y!=0

y!=0/16

y!=0

y∈R



Domain of the equation: y+3)!=0

y∈R


We get rid of parentheses

3/16y-1/y-3=0

We calculate fractions


3y/16y^2+(-16y)/16y^2-3=0

We multiply all the terms by the denominator


3y+(-16y)-3*16y^2=0

Wy multiply elements

-48y^2+3y+(-16y)=0

We get rid of parentheses

-48y^2+3y-16y=0

We add all the numbers together, and all the variables

-48y^2-13y=0

a = -48; b = -13; c = 0;
Δ = b2-4ac
Δ = -132-4·(-48)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-13}{2*-48}=\frac{0}{-96}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+13}{2*-48}=\frac{26}{-96}
=-13/48
$