5/(3y)-2/3=(51y)/(2y)

Solution for 5/(3y)-2/3=(51y)/(2y) equation:

5/(3y)-2/3=(51y)/(2y)

We move all terms to the left:

5/(3y)-2/3-((51y)/(2y))=0


Domain of the equation: 3y!=0

y!=0/3

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

5/3y-(+51y/2y)-2/3=0

We get rid of parentheses

5/3y-51y/2y-2/3=0

We calculate fractions


(-1377y^2)/54y^2+10y/54y^2+(-4y)/54y^2=0

We multiply all the terms by the denominator


(-1377y^2)+10y+(-4y)=0

We get rid of parentheses

-1377y^2+10y-4y=0

We add all the numbers together, and all the variables

-1377y^2+6y=0

a = -1377; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-1377)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-1377}=\frac{-12}{-2754}
=2/459
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-1377}=\frac{0}{-2754}
=0
$