-1/3y+2+3y=6

Solution for -1/3y+2+3y=6 equation:

-1/3y+2+3y=6

We move all terms to the left:

-1/3y+2+3y-(6)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We add all the numbers together, and all the variables

3y-1/3y-4=0

We multiply all the terms by the denominator


3y*3y-4*3y-1=0

Wy multiply elements

9y^2-12y-1=0

a = 9; b = -12; c = -1;
Δ = b2-4ac
Δ = -122-4·9·(-1)
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{5}}{2*9}=\frac{12-6\sqrt{5}}{18}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{5}}{2*9}=\frac{12+6\sqrt{5}}{18}
$