2(x^2-288)=0

Solution for 2(x^2-288)=0 equation:

2(x^2-288)=0

We multiply parentheses

2x^2-576=0

a = 2; b = 0; c = -576;
Δ = b2-4ac
Δ = 02-4·2·(-576)
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*2}=\frac{0-48\sqrt{2}}{4}
=-\frac{48\sqrt{2}}{4}
=-12\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+48\sqrt{2}}{2*2}=\frac{0+48\sqrt{2}}{4}
=\frac{48\sqrt{2}}{4}
=12\sqrt{2}
$