-1/3y+12=-0.5+12y

Solution for -1/3y+12=-0.5+12y equation:

-1/3y+12=-0.5+12y

We move all terms to the left:

-1/3y+12-(-0.5+12y)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We add all the numbers together, and all the variables

-1/3y-(12y-0.5)+12=0

We get rid of parentheses

-1/3y-12y+0.5+12=0

We multiply all the terms by the denominator


-12y*3y+(0.5)*3y+12*3y-1=0

We multiply parentheses

-12y*3y+1.5y+12*3y-1=0

Wy multiply elements

-36y^2+1.5y+36y-1=0

We add all the numbers together, and all the variables

-36y^2+37.5y-1=0

a = -36; b = 37.5; c = -1;
Δ = b2-4ac
Δ = 37.52-4·(-36)·(-1)
Δ = 1262.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(37.5)-\sqrt{1262.25}}{2*-36}=\frac{-37.5-\sqrt{1262.25}}{-72}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37.5)+\sqrt{1262.25}}{2*-36}=\frac{-37.5+\sqrt{1262.25}}{-72}
$