12y^2=9-12y

Solution for 12y^2=9-12y equation:

12y^2=9-12y

We move all terms to the left:

12y^2-(9-12y)=0

We add all the numbers together, and all the variables

12y^2-(-12y+9)=0

We get rid of parentheses

12y^2+12y-9=0

a = 12; b = 12; c = -9;
Δ = b2-4ac
Δ = 122-4·12·(-9)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-24}{2*12}=\frac{-36}{24}
=-1+1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+24}{2*12}=\frac{12}{24}
=1/2
$