-48x^2+256=0

Solution for -48x^2+256=0 equation:

-48x^2+256=0

a = -48; b = 0; c = +256;
Δ = b2-4ac
Δ = 02-4·(-48)·256
Δ = 49152
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:

$\sqrt{\Delta}=\sqrt{49152}=\sqrt{16384*3}=\sqrt{16384}*\sqrt{3}=128\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-128\sqrt{3}}{2*-48}=\frac{0-128\sqrt{3}}{-96}
=-\frac{128\sqrt{3}}{-96}
=-\frac{4\sqrt{3}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+128\sqrt{3}}{2*-48}=\frac{0+128\sqrt{3}}{-96}
=\frac{128\sqrt{3}}{-96}
=\frac{4\sqrt{3}}{-3}
$