-6t^2+64+192=0

Solution for -6t^2+64+192=0 equation:

-6t^2+64+192=0

We add all the numbers together, and all the variables

-6t^2+256=0

a = -6; b = 0; c = +256;
Δ = b2-4ac
Δ = 02-4·(-6)·256
Δ = 6144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{6144}=\sqrt{1024*6}=\sqrt{1024}*\sqrt{6}=32\sqrt{6}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32\sqrt{6}}{2*-6}=\frac{0-32\sqrt{6}}{-12}
=-\frac{32\sqrt{6}}{-12}
=-\frac{8\sqrt{6}}{-3}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32\sqrt{6}}{2*-6}=\frac{0+32\sqrt{6}}{-12}
=\frac{32\sqrt{6}}{-12}
=\frac{8\sqrt{6}}{-3}
$