1/2y+8=1/5y

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Solution for 1/2y+8=1/5y equation:



1/2y+8=1/5y
We move all terms to the left:
1/2y+8-(1/5y)=0
Domain of the equation: 2y!=0
y!=0/2
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
1/2y-(+1/5y)+8=0
We get rid of parentheses
1/2y-1/5y+8=0
We calculate fractions
5y/10y^2+(-2y)/10y^2+8=0
We multiply all the terms by the denominator
5y+(-2y)+8*10y^2=0
Wy multiply elements
80y^2+5y+(-2y)=0
We get rid of parentheses
80y^2+5y-2y=0
We add all the numbers together, and all the variables
80y^2+3y=0
a = 80; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·80·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*80}=\frac{-6}{160} =-3/80 $
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*80}=\frac{0}{160} =0 $

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