2/3y-1/4=5/6y+1

Solution for 2/3y-1/4=5/6y+1 equation:

2/3y-1/4=5/6y+1

We move all terms to the left:

2/3y-1/4-(5/6y+1)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R



Domain of the equation: 6y+1)!=0

y∈R


We get rid of parentheses

2/3y-5/6y-1-1/4=0

We calculate fractions


(-108y^2)/288y^2+192y/288y^2+(-240y)/288y^2-1=0

We multiply all the terms by the denominator


(-108y^2)+192y+(-240y)-1*288y^2=0

Wy multiply elements

(-108y^2)-288y^2+192y+(-240y)=0

We get rid of parentheses

-108y^2-288y^2+192y-240y=0

We add all the numbers together, and all the variables

-396y^2-48y=0

a = -396; b = -48; c = 0;
Δ = b2-4ac
Δ = -482-4·(-396)·0
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-48}{2*-396}=\frac{0}{-792}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+48}{2*-396}=\frac{96}{-792}
=-4/33
$