(60/y)=2y

Solution for (60/y)=2y equation:

(60/y)=2y

We move all terms to the left:

(60/y)-(2y)=0


Domain of the equation: y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

(+60/y)-2y=0

We add all the numbers together, and all the variables

-2y+(+60/y)=0

We get rid of parentheses

-2y+60/y=0

We multiply all the terms by the denominator


-2y*y+60=0

Wy multiply elements

-2y^2+60=0

a = -2; b = 0; c = +60;
Δ = b2-4ac
Δ = 02-4·(-2)·60
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{30}}{2*-2}=\frac{0-4\sqrt{30}}{-4}
=-\frac{4\sqrt{30}}{-4}
=-\frac{\sqrt{30}}{-1}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{30}}{2*-2}=\frac{0+4\sqrt{30}}{-4}
=\frac{4\sqrt{30}}{-4}
=\frac{\sqrt{30}}{-1}
$