(1/2y)-2=1/9y

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Solution for (1/2y)-2=1/9y equation:



(1/2y)-2=1/9y
We move all terms to the left:
(1/2y)-2-(1/9y)=0
Domain of the equation: 2y)!=0
y!=0/1
y!=0
y∈R
Domain of the equation: 9y)!=0
y!=0/1
y!=0
y∈R
We add all the numbers together, and all the variables
(+1/2y)-(+1/9y)-2=0
We get rid of parentheses
1/2y-1/9y-2=0
We calculate fractions
9y/18y^2+(-2y)/18y^2-2=0
We multiply all the terms by the denominator
9y+(-2y)-2*18y^2=0
Wy multiply elements
-36y^2+9y+(-2y)=0
We get rid of parentheses
-36y^2+9y-2y=0
We add all the numbers together, and all the variables
-36y^2+7y=0
a = -36; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-36)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-36}=\frac{-14}{-72} =7/36 $
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-36}=\frac{0}{-72} =0 $

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