3/10y=1+1/3y

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

3/10y=1+1/3y

We move all terms to the left:

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


Domain of the equation: 10y!=0

y!=0/10

y!=0

y∈R



Domain of the equation: 3y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


9y/30y^2+(-10y)/30y^2-1=0

We multiply all the terms by the denominator


9y+(-10y)-1*30y^2=0

Wy multiply elements

-30y^2+9y+(-10y)=0

We get rid of parentheses

-30y^2+9y-10y=0

We add all the numbers together, and all the variables

-30y^2-1y=0

a = -30; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-30)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*-30}=\frac{0}{-60}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-30}=\frac{2}{-60}
=-1/30
$