1/4y-11=1/5y

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Solution for 1/4y-11=1/5y equation:



1/4y-11=1/5y
We move all terms to the left:
1/4y-11-(1/5y)=0
Domain of the equation: 4y!=0
y!=0/4
y!=0
y∈R
Domain of the equation: 5y)!=0
y!=0/1
y!=0
y∈R
We add all the numbers together, and all the variables
1/4y-(+1/5y)-11=0
We get rid of parentheses
1/4y-1/5y-11=0
We calculate fractions
5y/20y^2+(-4y)/20y^2-11=0
We multiply all the terms by the denominator
5y+(-4y)-11*20y^2=0
Wy multiply elements
-220y^2+5y+(-4y)=0
We get rid of parentheses
-220y^2+5y-4y=0
We add all the numbers together, and all the variables
-220y^2+y=0
a = -220; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-220)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-220}=\frac{-2}{-440} =1/220 $
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-220}=\frac{0}{-440} =0 $

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