580/580-y+580/y=9

Solution for 580/580-y+580/y=9 equation:

580/580-y+580/y=9

We move all terms to the left:

580/580-y+580/y-(9)=0


Domain of the equation: y!=0

y∈R


determiningTheFunctionDomain
-y+580/y-9+580/580=0

We add all the numbers together, and all the variables

-1y+580/y-8=0

We multiply all the terms by the denominator


-1y*y-8*y+580=0

We add all the numbers together, and all the variables

-8y-1y*y+580=0

Wy multiply elements

-1y^2-8y+580=0

a = -1; b = -8; c = +580;
Δ = b2-4ac
Δ = -82-4·(-1)·580
Δ = 2384
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2384}=\sqrt{16*149}=\sqrt{16}*\sqrt{149}=4\sqrt{149}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{149}}{2*-1}=\frac{8-4\sqrt{149}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{149}}{2*-1}=\frac{8+4\sqrt{149}}{-2}
$