12-y=1/3y

Solution for 12-y=1/3y equation:

12-y=1/3y

We move all terms to the left:

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


Domain of the equation: 3y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

-y-(+1/3y)+12=0

We add all the numbers together, and all the variables

-1y-(+1/3y)+12=0

We get rid of parentheses

-1y-1/3y+12=0

We multiply all the terms by the denominator


-1y*3y+12*3y-1=0

Wy multiply elements

-3y^2+36y-1=0

a = -3; b = 36; c = -1;
Δ = b2-4ac
Δ = 362-4·(-3)·(-1)
Δ = 1284
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:

$\sqrt{\Delta}=\sqrt{1284}=\sqrt{4*321}=\sqrt{4}*\sqrt{321}=2\sqrt{321}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-2\sqrt{321}}{2*-3}=\frac{-36-2\sqrt{321}}{-6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+2\sqrt{321}}{2*-3}=\frac{-36+2\sqrt{321}}{-6}
$