2/3y-3=5-2y

Solution for 2/3y-3=5-2y equation:

2/3y-3=5-2y

We move all terms to the left:

2/3y-3-(5-2y)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We add all the numbers together, and all the variables

2/3y-(-2y+5)-3=0

We get rid of parentheses

2/3y+2y-5-3=0

We multiply all the terms by the denominator


2y*3y-5*3y-3*3y+2=0

Wy multiply elements

6y^2-15y-9y+2=0

We add all the numbers together, and all the variables

6y^2-24y+2=0

a = 6; b = -24; c = +2;
Δ = b2-4ac
Δ = -242-4·6·2
Δ = 528
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:

$\sqrt{\Delta}=\sqrt{528}=\sqrt{16*33}=\sqrt{16}*\sqrt{33}=4\sqrt{33}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{33}}{2*6}=\frac{24-4\sqrt{33}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{33}}{2*6}=\frac{24+4\sqrt{33}}{12}
$