3/10y=1/y+13

Solution for 3/10y=1/y+13 equation:

3/10y=1/y+13

We move all terms to the left:

3/10y-(1/y+13)=0


Domain of the equation: 10y!=0

y!=0/10

y!=0

y∈R



Domain of the equation: y+13)!=0

y∈R


We get rid of parentheses

3/10y-1/y-13=0

We calculate fractions


3y/10y^2+(-10y)/10y^2-13=0

We multiply all the terms by the denominator


3y+(-10y)-13*10y^2=0

Wy multiply elements

-130y^2+3y+(-10y)=0

We get rid of parentheses

-130y^2+3y-10y=0

We add all the numbers together, and all the variables

-130y^2-7y=0

a = -130; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·(-130)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*-130}=\frac{0}{-260}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*-130}=\frac{14}{-260}
=-7/130
$