-16x^2+48+288=0

Solution for -16x^2+48+288=0 equation:

-16x^2+48+288=0

We add all the numbers together, and all the variables

-16x^2+336=0

a = -16; b = 0; c = +336;
Δ = b2-4ac
Δ = 02-4·(-16)·336
Δ = 21504
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:

$\sqrt{\Delta}=\sqrt{21504}=\sqrt{1024*21}=\sqrt{1024}*\sqrt{21}=32\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32\sqrt{21}}{2*-16}=\frac{0-32\sqrt{21}}{-32}
=-\frac{32\sqrt{21}}{-32}
=-\frac{\sqrt{21}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32\sqrt{21}}{2*-16}=\frac{0+32\sqrt{21}}{-32}
=\frac{32\sqrt{21}}{-32}
=\frac{\sqrt{21}}{-1}
$