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

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

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

We move all terms to the left:

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


Domain of the equation: 6y!=0

y!=0/6

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

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

We get rid of parentheses

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

We calculate fractions


(-162y^2)/216y^2+180y/216y^2+(-48y)/216y^2+(-96y)/216y^2=0

We multiply all the terms by the denominator


(-162y^2)+180y+(-48y)+(-96y)=0

We get rid of parentheses

-162y^2+180y-48y-96y=0

We add all the numbers together, and all the variables

-162y^2+36y=0

a = -162; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·(-162)·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-36}{2*-162}=\frac{-72}{-324}
=2/9
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*-162}=\frac{0}{-324}
=0
$