5+2/3y=y+2

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

5+2/3y=y+2

We move all terms to the left:

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


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-3y^2-6y+15y+2=0

We add all the numbers together, and all the variables

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

a = -3; b = 9; c = +2;
Δ = b2-4ac
Δ = 92-4·(-3)·2
Δ = 105
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{-(9)-\sqrt{105}}{2*-3}=\frac{-9-\sqrt{105}}{-6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{105}}{2*-3}=\frac{-9+\sqrt{105}}{-6}
$