y=360/y

Solution for y=360/y equation:

y=360/y

We move all terms to the left:

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

We get rid of parentheses

y-360/y=0

We multiply all the terms by the denominator


y*y-360=0

Wy multiply elements

y^2-360=0

a = 1; b = 0; c = -360;
Δ = b2-4ac
Δ = 02-4·1·(-360)
Δ = 1440
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:

$\sqrt{\Delta}=\sqrt{1440}=\sqrt{144*10}=\sqrt{144}*\sqrt{10}=12\sqrt{10}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{10}}{2*1}=\frac{0-12\sqrt{10}}{2}
=-\frac{12\sqrt{10}}{2}
=-6\sqrt{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{10}}{2*1}=\frac{0+12\sqrt{10}}{2}
=\frac{12\sqrt{10}}{2}
=6\sqrt{10}
$