8/5y=64/y-3

Solution for 8/5y=64/y-3 equation:

8/5y=64/y-3

We move all terms to the left:

8/5y-(64/y-3)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R



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

y∈R


We get rid of parentheses

8/5y-64/y+3=0

We calculate fractions


8y/5y^2+(-320y)/5y^2+3=0

We multiply all the terms by the denominator


8y+(-320y)+3*5y^2=0

Wy multiply elements

15y^2+8y+(-320y)=0

We get rid of parentheses

15y^2+8y-320y=0

We add all the numbers together, and all the variables

15y^2-312y=0

a = 15; b = -312; c = 0;
Δ = b2-4ac
Δ = -3122-4·15·0
Δ = 97344
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{97344}=312$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-312)-312}{2*15}=\frac{0}{30}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-312)+312}{2*15}=\frac{624}{30}
=20+4/5
$