2/3y+1/6=-3/4y+1

Solution for 2/3y+1/6=-3/4y+1 equation:

2/3y+1/6=-3/4y+1

We move all terms to the left:

2/3y+1/6-(-3/4y+1)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R



Domain of the equation: 4y+1)!=0

y∈R


We get rid of parentheses

2/3y+3/4y-1+1/6=0

We calculate fractions


48y^2/432y^2+288y/432y^2+324y/432y^2-1=0

We multiply all the terms by the denominator


48y^2+288y+324y-1*432y^2=0

We add all the numbers together, and all the variables

48y^2+612y-1*432y^2=0

Wy multiply elements

48y^2-432y^2+612y=0

We add all the numbers together, and all the variables

-384y^2+612y=0

a = -384; b = 612; c = 0;
Δ = b2-4ac
Δ = 6122-4·(-384)·0
Δ = 374544
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{374544}=612$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(612)-612}{2*-384}=\frac{-1224}{-768}
=1+19/32
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(612)+612}{2*-384}=\frac{0}{-768}
=0
$