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

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

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

We move all terms to the left:

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


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-54y^2)/96y^2+48y/96y^2+(-64y)/96y^2=0

We multiply all the terms by the denominator


(-54y^2)+48y+(-64y)=0

We get rid of parentheses

-54y^2+48y-64y=0

We add all the numbers together, and all the variables

-54y^2-16y=0

a = -54; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·(-54)·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*-54}=\frac{0}{-108}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*-54}=\frac{32}{-108}
=-8/27
$