1/(3y)=y-60

Solution for 1/(3y)=y-60 equation:

1/(3y)=y-60

We move all terms to the left:

1/(3y)-(y-60)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We get rid of parentheses

1/3y-y+60=0

We multiply all the terms by the denominator


-y*3y+60*3y+1=0

Wy multiply elements

-3y^2+180y+1=0

a = -3; b = 180; c = +1;
Δ = b2-4ac
Δ = 1802-4·(-3)·1
Δ = 32412
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:

$\sqrt{\Delta}=\sqrt{32412}=\sqrt{4*8103}=\sqrt{4}*\sqrt{8103}=2\sqrt{8103}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-2\sqrt{8103}}{2*-3}=\frac{-180-2\sqrt{8103}}{-6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+2\sqrt{8103}}{2*-3}=\frac{-180+2\sqrt{8103}}{-6}
$