y-9+(2/y)=180

Solution for y-9+(2/y)=180 equation:

y-9+(2/y)=180

We move all terms to the left:

y-9+(2/y)-(180)=0


Domain of the equation: y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

y+(+2/y)-9-180=0

We add all the numbers together, and all the variables

y+(+2/y)-189=0

We get rid of parentheses

y+2/y-189=0

We multiply all the terms by the denominator


y*y-189*y+2=0

We add all the numbers together, and all the variables

-189y+y*y+2=0

Wy multiply elements

y^2-189y+2=0

a = 1; b = -189; c = +2;
Δ = b2-4ac
Δ = -1892-4·1·2
Δ = 35713
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-189)-\sqrt{35713}}{2*1}=\frac{189-\sqrt{35713}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-189)+\sqrt{35713}}{2*1}=\frac{189+\sqrt{35713}}{2}
$