-16t^2+192t=300

Solution for -16t^2+192t=300 equation:

-16t^2+192t=300

We move all terms to the left:

-16t^2+192t-(300)=0

a = -16; b = 192; c = -300;
Δ = b2-4ac
Δ = 1922-4·(-16)·(-300)
Δ = 17664
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:

$\sqrt{\Delta}=\sqrt{17664}=\sqrt{256*69}=\sqrt{256}*\sqrt{69}=16\sqrt{69}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(192)-16\sqrt{69}}{2*-16}=\frac{-192-16\sqrt{69}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(192)+16\sqrt{69}}{2*-16}=\frac{-192+16\sqrt{69}}{-32}
$