3y^2-12y=21

Solution for 3y^2-12y=21 equation:

3y^2-12y=21

We move all terms to the left:

3y^2-12y-(21)=0

a = 3; b = -12; c = -21;
Δ = b2-4ac
Δ = -122-4·3·(-21)
Δ = 396
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:

$\sqrt{\Delta}=\sqrt{396}=\sqrt{36*11}=\sqrt{36}*\sqrt{11}=6\sqrt{11}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{11}}{2*3}=\frac{12-6\sqrt{11}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{11}}{2*3}=\frac{12+6\sqrt{11}}{6}
$