384=6y^2

Solution for 384=6y^2 equation:

384=6y^2

We move all terms to the left:

384-(6y^2)=0

a = -6; b = 0; c = +384;
Δ = b2-4ac
Δ = 02-4·(-6)·384
Δ = 9216
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9216}=96$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-96}{2*-6}=\frac{-96}{-12}
=+8
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+96}{2*-6}=\frac{96}{-12}
=-8
$