13/10y+1/20y-7/4=4/5

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Solution for 13/10y+1/20y-7/4=4/5 equation:



13/10y+1/20y-7/4=4/5
We move all terms to the left:
13/10y+1/20y-7/4-(4/5)=0
Domain of the equation: 10y!=0
y!=0/10
y!=0
y∈R
Domain of the equation: 20y!=0
y!=0/20
y!=0
y∈R
We add all the numbers together, and all the variables
13/10y+1/20y-7/4-(+4/5)=0
We get rid of parentheses
13/10y+1/20y-7/4-4/5=0
We calculate fractions
(-14000y^2)/16000y^2+(-6400y^2)/16000y^2+20800y/16000y^2+800y/16000y^2=0
We multiply all the terms by the denominator
(-14000y^2)+(-6400y^2)+20800y+800y=0
We add all the numbers together, and all the variables
(-14000y^2)+(-6400y^2)+21600y=0
We get rid of parentheses
-14000y^2-6400y^2+21600y=0
We add all the numbers together, and all the variables
-20400y^2+21600y=0
a = -20400; b = 21600; c = 0;
Δ = b2-4ac
Δ = 216002-4·(-20400)·0
Δ = 466560000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{466560000}=21600$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21600)-21600}{2*-20400}=\frac{-43200}{-40800} =1+1/17 $
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21600)+21600}{2*-20400}=\frac{0}{-40800} =0 $

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