2(60-1/3y)+(y+6-1/3y)=180

Solution for 2(60-1/3y)+(y+6-1/3y)=180 equation:

2(60-1/3y)+(y+6-1/3y)=180

We move all terms to the left:

2(60-1/3y)+(y+6-1/3y)-(180)=0


Domain of the equation: 3y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

2(-1/3y+60)+(y-1/3y+6)-180=0

We multiply parentheses

-2y+(y-1/3y+6)+120-180=0

We get rid of parentheses

-2y+y-1/3y+6+120-180=0

We multiply all the terms by the denominator


-2y*3y+y*3y+6*3y+120*3y-180*3y-1=0

Wy multiply elements

-6y^2+3y^2+18y+360y-540y-1=0

We add all the numbers together, and all the variables

-3y^2-162y-1=0

a = -3; b = -162; c = -1;
Δ = b2-4ac
Δ = -1622-4·(-3)·(-1)
Δ = 26232
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:

$\sqrt{\Delta}=\sqrt{26232}=\sqrt{4*6558}=\sqrt{4}*\sqrt{6558}=2\sqrt{6558}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-162)-2\sqrt{6558}}{2*-3}=\frac{162-2\sqrt{6558}}{-6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-162)+2\sqrt{6558}}{2*-3}=\frac{162+2\sqrt{6558}}{-6}
$