9-2/3y=y

Solution for 9-2/3y=y equation:

9-2/3y=y

We move all terms to the left:

9-2/3y-(y)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We add all the numbers together, and all the variables

-1y-2/3y+9=0

We multiply all the terms by the denominator


-1y*3y+9*3y-2=0

Wy multiply elements

-3y^2+27y-2=0

a = -3; b = 27; c = -2;
Δ = b2-4ac
Δ = 272-4·(-3)·(-2)
Δ = 705
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-\sqrt{705}}{2*-3}=\frac{-27-\sqrt{705}}{-6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+\sqrt{705}}{2*-3}=\frac{-27+\sqrt{705}}{-6}
$