16x2-512=0

Solution for 16x2-512=0 equation:

16x^2-512=0

a = 16; b = 0; c = -512;
Δ = b2-4ac
Δ = 02-4·16·(-512)
Δ = 32768
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:

$\sqrt{\Delta}=\sqrt{32768}=\sqrt{16384*2}=\sqrt{16384}*\sqrt{2}=128\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-128\sqrt{2}}{2*16}=\frac{0-128\sqrt{2}}{32}
=-\frac{128\sqrt{2}}{32}
=-4\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+128\sqrt{2}}{2*16}=\frac{0+128\sqrt{2}}{32}
=\frac{128\sqrt{2}}{32}
=4\sqrt{2}
$