y-3=2/3y+3

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

y-3=2/3y+3

We move all terms to the left:

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


Domain of the equation: 3y+3)!=0

y∈R


We get rid of parentheses

y-2/3y-3-3=0

We multiply all the terms by the denominator


y*3y-3*3y-3*3y-2=0

Wy multiply elements

3y^2-9y-9y-2=0

We add all the numbers together, and all the variables

3y^2-18y-2=0

a = 3; b = -18; c = -2;
Δ = b2-4ac
Δ = -182-4·3·(-2)
Δ = 348
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{348}=\sqrt{4*87}=\sqrt{4}*\sqrt{87}=2\sqrt{87}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{87}}{2*3}=\frac{18-2\sqrt{87}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{87}}{2*3}=\frac{18+2\sqrt{87}}{6}
$