5/2y-3=7/3y

Solution for 5/2y-3=7/3y equation:

5/2y-3=7/3y

We move all terms to the left:

5/2y-3-(7/3y)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 3y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

5/2y-(+7/3y)-3=0

We get rid of parentheses

5/2y-7/3y-3=0

We calculate fractions


15y/6y^2+(-14y)/6y^2-3=0

We multiply all the terms by the denominator


15y+(-14y)-3*6y^2=0

Wy multiply elements

-18y^2+15y+(-14y)=0

We get rid of parentheses

-18y^2+15y-14y=0

We add all the numbers together, and all the variables

-18y^2+y=0

a = -18; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-18)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-18}=\frac{-2}{-36}
=1/18
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-18}=\frac{0}{-36}
=0
$