1/4y-2=1/9y

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Solution for 1/4y-2=1/9y equation:



1/4y-2=1/9y
We move all terms to the left:
1/4y-2-(1/9y)=0
Domain of the equation: 4y!=0
y!=0/4
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
1/4y-(+1/9y)-2=0
We get rid of parentheses
1/4y-1/9y-2=0
We calculate fractions
9y/36y^2+(-4y)/36y^2-2=0
We multiply all the terms by the denominator
9y+(-4y)-2*36y^2=0
Wy multiply elements
-72y^2+9y+(-4y)=0
We get rid of parentheses
-72y^2+9y-4y=0
We add all the numbers together, and all the variables
-72y^2+5y=0
a = -72; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-72)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-72}=\frac{-10}{-144} =5/72 $
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-72}=\frac{0}{-144} =0 $

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