-16x^2+192=0

Solution for -16x^2+192=0 equation:

-16x^2+192=0

a = -16; b = 0; c = +192;
Δ = b2-4ac
Δ = 02-4·(-16)·192
Δ = 12288
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:

$\sqrt{\Delta}=\sqrt{12288}=\sqrt{4096*3}=\sqrt{4096}*\sqrt{3}=64\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-64\sqrt{3}}{2*-16}=\frac{0-64\sqrt{3}}{-32}
=-\frac{64\sqrt{3}}{-32}
=-\frac{2\sqrt{3}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+64\sqrt{3}}{2*-16}=\frac{0+64\sqrt{3}}{-32}
=\frac{64\sqrt{3}}{-32}
=\frac{2\sqrt{3}}{-1}
$