2/3y+y=3

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

2/3y+y=3

We move all terms to the left:

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


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We add all the numbers together, and all the variables

y+2/3y-3=0

We multiply all the terms by the denominator


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

Wy multiply elements

3y^2-9y+2=0

a = 3; b = -9; c = +2;
Δ = b2-4ac
Δ = -92-4·3·2
Δ = 57
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{57}}{2*3}=\frac{9-\sqrt{57}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{57}}{2*3}=\frac{9+\sqrt{57}}{6}
$