1/20+5/4y=3/5y

Solution for 1/20+5/4y=3/5y equation:

1/20+5/4y=3/5y

We move all terms to the left:

1/20+5/4y-(3/5y)=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

5/4y-(+3/5y)+1/20=0

We get rid of parentheses

5/4y-3/5y+1/20=0

We calculate fractions


100y^2/800y^2+1000y/800y^2+(-480y)/800y^2=0

We multiply all the terms by the denominator


100y^2+1000y+(-480y)=0

We get rid of parentheses

100y^2+1000y-480y=0

We add all the numbers together, and all the variables

100y^2+520y=0

a = 100; b = 520; c = 0;
Δ = b2-4ac
Δ = 5202-4·100·0
Δ = 270400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{270400}=520$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(520)-520}{2*100}=\frac{-1040}{200}
=-5+1/5
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(520)+520}{2*100}=\frac{0}{200}
=0
$