3/5y=1/10y+200

Solution for 3/5y=1/10y+200 equation:

3/5y=1/10y+200

We move all terms to the left:

3/5y-(1/10y+200)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R



Domain of the equation: 10y+200)!=0

y∈R


We get rid of parentheses

3/5y-1/10y-200=0

We calculate fractions


30y/50y^2+(-5y)/50y^2-200=0

We multiply all the terms by the denominator


30y+(-5y)-200*50y^2=0

Wy multiply elements

-10000y^2+30y+(-5y)=0

We get rid of parentheses

-10000y^2+30y-5y=0

We add all the numbers together, and all the variables

-10000y^2+25y=0

a = -10000; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·(-10000)·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*-10000}=\frac{-50}{-20000}
=1/400
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*-10000}=\frac{0}{-20000}
=0
$