2/5y-3/4=3/20y

Solution for 2/5y-3/4=3/20y equation:

2/5y-3/4=3/20y

We move all terms to the left:

2/5y-3/4-(3/20y)=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

2/5y-(+3/20y)-3/4=0

We get rid of parentheses

2/5y-3/20y-3/4=0

We calculate fractions


(-600y^2)/1600y^2+640y/1600y^2+(-240y)/1600y^2=0

We multiply all the terms by the denominator


(-600y^2)+640y+(-240y)=0

We get rid of parentheses

-600y^2+640y-240y=0

We add all the numbers together, and all the variables

-600y^2+400y=0

a = -600; b = 400; c = 0;
Δ = b2-4ac
Δ = 4002-4·(-600)·0
Δ = 160000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{160000}=400$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(400)-400}{2*-600}=\frac{-800}{-1200}
=2/3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(400)+400}{2*-600}=\frac{0}{-1200}
=0
$