(360/y-2)(y+2)=360

Solution for (360/y-2)(y+2)=360 equation:

(360/y-2)(y+2)=360

We move all terms to the left:

(360/y-2)(y+2)-(360)=0


Domain of the equation: y-2)(y+2)!=0

y∈R


We multiply parentheses ..

(+360y^2+720y-2y-4)-360=0

We get rid of parentheses

360y^2+720y-2y-4-360=0

We add all the numbers together, and all the variables

360y^2+718y-364=0

a = 360; b = 718; c = -364;
Δ = b2-4ac
Δ = 7182-4·360·(-364)
Δ = 1039684
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:

$\sqrt{\Delta}=\sqrt{1039684}=\sqrt{4*259921}=\sqrt{4}*\sqrt{259921}=2\sqrt{259921}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(718)-2\sqrt{259921}}{2*360}=\frac{-718-2\sqrt{259921}}{720}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(718)+2\sqrt{259921}}{2*360}=\frac{-718+2\sqrt{259921}}{720}
$