2/3y+12=1/6y-9

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Solution for 2/3y+12=1/6y-9 equation:



2/3y+12=1/6y-9
We move all terms to the left:
2/3y+12-(1/6y-9)=0
Domain of the equation: 3y!=0
y!=0/3
y!=0
y∈R
Domain of the equation: 6y-9)!=0
y∈R
We get rid of parentheses
2/3y-1/6y+9+12=0
We calculate fractions
12y/18y^2+(-3y)/18y^2+9+12=0
We add all the numbers together, and all the variables
12y/18y^2+(-3y)/18y^2+21=0
We multiply all the terms by the denominator
12y+(-3y)+21*18y^2=0
Wy multiply elements
378y^2+12y+(-3y)=0
We get rid of parentheses
378y^2+12y-3y=0
We add all the numbers together, and all the variables
378y^2+9y=0
a = 378; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·378·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*378}=\frac{-18}{756} =-1/42 $
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*378}=\frac{0}{756} =0 $

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