1/10y+9=3/5y-1

Solution for 1/10y+9=3/5y-1 equation:

1/10y+9=3/5y-1

We move all terms to the left:

1/10y+9-(3/5y-1)=0


Domain of the equation: 10y!=0

y!=0/10

y!=0

y∈R



Domain of the equation: 5y-1)!=0

y∈R


We get rid of parentheses

1/10y-3/5y+1+9=0

We calculate fractions


5y/50y^2+(-30y)/50y^2+1+9=0

We add all the numbers together, and all the variables

5y/50y^2+(-30y)/50y^2+10=0

We multiply all the terms by the denominator


5y+(-30y)+10*50y^2=0

Wy multiply elements

500y^2+5y+(-30y)=0

We get rid of parentheses

500y^2+5y-30y=0

We add all the numbers together, and all the variables

500y^2-25y=0

a = 500; b = -25; c = 0;
Δ = b2-4ac
Δ = -252-4·500·0
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*500}=\frac{0}{1000}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+25}{2*500}=\frac{50}{1000}
=1/20
$