1/y+3/8=5/2y

Solution for 1/y+3/8=5/2y equation:

1/y+3/8=5/2y

We move all terms to the left:

1/y+3/8-(5/2y)=0


Domain of the equation: y!=0

y∈R



Domain of the equation: 2y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

1/y-(+5/2y)+3/8=0

We get rid of parentheses

1/y-5/2y+3/8=0

We calculate fractions


12y^2/128y^2+128y/128y^2+(-320y)/128y^2=0

We multiply all the terms by the denominator


12y^2+128y+(-320y)=0

We get rid of parentheses

12y^2+128y-320y=0

We add all the numbers together, and all the variables

12y^2-192y=0

a = 12; b = -192; c = 0;
Δ = b2-4ac
Δ = -1922-4·12·0
Δ = 36864
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36864}=192$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-192)-192}{2*12}=\frac{0}{24}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-192)+192}{2*12}=\frac{384}{24}
=16
$