-1/2y+12=0.5+12y

Solution for -1/2y+12=0.5+12y equation:

-1/2y+12=0.5+12y

We move all terms to the left:

-1/2y+12-(0.5+12y)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We add all the numbers together, and all the variables

-1/2y-(12y+0.5)+12=0

We get rid of parentheses

-1/2y-12y-0.5+12=0

We multiply all the terms by the denominator


-12y*2y-(0.5)*2y+12*2y-1=0

We multiply parentheses

-12y*2y-y+12*2y-1=0

Wy multiply elements

-24y^2-y+24y-1=0

We add all the numbers together, and all the variables

-24y^2+23y-1=0

a = -24; b = 23; c = -1;
Δ = b2-4ac
Δ = 232-4·(-24)·(-1)
Δ = 433
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{-(23)-\sqrt{433}}{2*-24}=\frac{-23-\sqrt{433}}{-48}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+\sqrt{433}}{2*-24}=\frac{-23+\sqrt{433}}{-48}
$