3y^2-12y=-3

Solution for 3y^2-12y=-3 equation:

3y^2-12y=-3

We move all terms to the left:

3y^2-12y-(-3)=0

We add all the numbers together, and all the variables

3y^2-12y+3=0

a = 3; b = -12; c = +3;
Δ = b2-4ac
Δ = -122-4·3·3
Δ = 108
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:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{3}}{2*3}=\frac{12-6\sqrt{3}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{3}}{2*3}=\frac{12+6\sqrt{3}}{6}
$