2/y=y/9y-40

Solution for 2/y=y/9y-40 equation:

2/y=y/9y-40

We move all terms to the left:

2/y-(y/9y-40)=0


Domain of the equation: y!=0

y∈R



Domain of the equation: 9y-40)!=0

y∈R


We get rid of parentheses

2/y-y/9y+40=0

We calculate fractions


(-1y^2)/9y^2+18y/9y^2+40=0

We multiply all the terms by the denominator


(-1y^2)+18y+40*9y^2=0

Wy multiply elements

(-1y^2)+360y^2+18y=0

We get rid of parentheses

-1y^2+360y^2+18y=0

We add all the numbers together, and all the variables

359y^2+18y=0

a = 359; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·359·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*359}=\frac{-36}{718}
=-18/359
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*359}=\frac{0}{718}
=0
$