344=16t^2+192

Solution for 344=16t^2+192 equation:

344=16t^2+192

We move all terms to the left:

344-(16t^2+192)=0

We get rid of parentheses

-16t^2-192+344=0

We add all the numbers together, and all the variables

-16t^2+152=0

a = -16; b = 0; c = +152;
Δ = b2-4ac
Δ = 02-4·(-16)·152
Δ = 9728
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:

$\sqrt{\Delta}=\sqrt{9728}=\sqrt{256*38}=\sqrt{256}*\sqrt{38}=16\sqrt{38}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{38}}{2*-16}=\frac{0-16\sqrt{38}}{-32}
=-\frac{16\sqrt{38}}{-32}
=-\frac{\sqrt{38}}{-2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{38}}{2*-16}=\frac{0+16\sqrt{38}}{-32}
=\frac{16\sqrt{38}}{-32}
=\frac{\sqrt{38}}{-2}
$