32y^2=384

Solution for 32y^2=384 equation:

32y^2=384

We move all terms to the left:

32y^2-(384)=0

a = 32; b = 0; c = -384;
Δ = b2-4ac
Δ = 02-4·32·(-384)
Δ = 49152
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:

$\sqrt{\Delta}=\sqrt{49152}=\sqrt{16384*3}=\sqrt{16384}*\sqrt{3}=128\sqrt{3}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-128\sqrt{3}}{2*32}=\frac{0-128\sqrt{3}}{64}
=-\frac{128\sqrt{3}}{64}
=-2\sqrt{3}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+128\sqrt{3}}{2*32}=\frac{0+128\sqrt{3}}{64}
=\frac{128\sqrt{3}}{64}
=2\sqrt{3}
$