2/3y+60=2y

Solution for 2/3y+60=2y equation:

2/3y+60=2y

We move all terms to the left:

2/3y+60-(2y)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We add all the numbers together, and all the variables

-2y+2/3y+60=0

We multiply all the terms by the denominator


-2y*3y+60*3y+2=0

Wy multiply elements

-6y^2+180y+2=0

a = -6; b = 180; c = +2;
Δ = b2-4ac
Δ = 1802-4·(-6)·2
Δ = 32448
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:

$\sqrt{\Delta}=\sqrt{32448}=\sqrt{10816*3}=\sqrt{10816}*\sqrt{3}=104\sqrt{3}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-104\sqrt{3}}{2*-6}=\frac{-180-104\sqrt{3}}{-12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+104\sqrt{3}}{2*-6}=\frac{-180+104\sqrt{3}}{-12}
$