3y2=32

Solution for 3y2=32 equation:

3y^2=32

We move all terms to the left:

3y^2-(32)=0

a = 3; b = 0; c = -32;
Δ = b2-4ac
Δ = 02-4·3·(-32)
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{6}}{2*3}=\frac{0-8\sqrt{6}}{6}
=-\frac{8\sqrt{6}}{6}
=-\frac{4\sqrt{6}}{3}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{6}}{2*3}=\frac{0+8\sqrt{6}}{6}
=\frac{8\sqrt{6}}{6}
=\frac{4\sqrt{6}}{3}
$