1/5y+7=17-1/20y

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Solution for 1/5y+7=17-1/20y equation:



1/5y+7=17-1/20y
We move all terms to the left:
1/5y+7-(17-1/20y)=0
Domain of the equation: 5y!=0
y!=0/5
y!=0
y∈R
Domain of the equation: 20y)!=0
y!=0/1
y!=0
y∈R
We add all the numbers together, and all the variables
1/5y-(-1/20y+17)+7=0
We get rid of parentheses
1/5y+1/20y-17+7=0
We calculate fractions
20y/100y^2+5y/100y^2-17+7=0
We add all the numbers together, and all the variables
20y/100y^2+5y/100y^2-10=0
We multiply all the terms by the denominator
20y+5y-10*100y^2=0
We add all the numbers together, and all the variables
25y-10*100y^2=0
Wy multiply elements
-1000y^2+25y=0
a = -1000; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·(-1000)·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*-1000}=\frac{-50}{-2000} =1/40 $
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*-1000}=\frac{0}{-2000} =0 $

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