3x^2-384=0

Solution for 3x^2-384=0 equation:

3x^2-384=0

a = 3; b = 0; c = -384;
Δ = b2-4ac
Δ = 02-4·3·(-384)
Δ = 4608
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4608}=\sqrt{2304*2}=\sqrt{2304}*\sqrt{2}=48\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-48\sqrt{2}}{2*3}=\frac{0-48\sqrt{2}}{6}
=-\frac{48\sqrt{2}}{6}
=-8\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+48\sqrt{2}}{2*3}=\frac{0+48\sqrt{2}}{6}
=\frac{48\sqrt{2}}{6}
=8\sqrt{2}
$