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

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

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

We move all terms to the left:

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


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R



Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-36y^2)/96y^2+64y/96y^2+(-48y)/96y^2=0

We multiply all the terms by the denominator


(-36y^2)+64y+(-48y)=0

We get rid of parentheses

-36y^2+64y-48y=0

We add all the numbers together, and all the variables

-36y^2+16y=0

a = -36; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·(-36)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*-36}=\frac{-32}{-72}
=4/9
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*-36}=\frac{0}{-72}
=0
$