3/4y+2/3=1/2y

Solution for 3/4y+2/3=1/2y equation:

3/4y+2/3=1/2y

We move all terms to the left:

3/4y+2/3-(1/2y)=0


Domain of the equation: 4y!=0

y!=0/4

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

3/4y-(+1/2y)+2/3=0

We get rid of parentheses

3/4y-1/2y+2/3=0

We calculate fractions


32y^2/72y^2+54y/72y^2+(-36y)/72y^2=0

We multiply all the terms by the denominator


32y^2+54y+(-36y)=0

We get rid of parentheses

32y^2+54y-36y=0

We add all the numbers together, and all the variables

32y^2+18y=0

a = 32; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·32·0
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*32}=\frac{-36}{64}
=-9/16
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*32}=\frac{0}{64}
=0
$