3/2y-4/3=5/4y

Solution for 3/2y-4/3=5/4y equation:

3/2y-4/3=5/4y

We move all terms to the left:

3/2y-4/3-(5/4y)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 4y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

3/2y-(+5/4y)-4/3=0

We get rid of parentheses

3/2y-5/4y-4/3=0

We calculate fractions


(-128y^2)/72y^2+108y/72y^2+(-90y)/72y^2=0

We multiply all the terms by the denominator


(-128y^2)+108y+(-90y)=0

We get rid of parentheses

-128y^2+108y-90y=0

We add all the numbers together, and all the variables

-128y^2+18y=0

a = -128; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·(-128)·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*-128}=\frac{-36}{-256}
=9/64
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*-128}=\frac{0}{-256}
=0
$