-6000*t^2-800*t+4800=0

Solution for -6000*t^2-800*t+4800=0 equation:

-6000t^2-800t+4800=0

a = -6000; b = -800; c = +4800;
Δ = b2-4ac
Δ = -8002-4·(-6000)·4800
Δ = 115840000
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:

$\sqrt{\Delta}=\sqrt{115840000}=\sqrt{640000*181}=\sqrt{640000}*\sqrt{181}=800\sqrt{181}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-800)-800\sqrt{181}}{2*-6000}=\frac{800-800\sqrt{181}}{-12000}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-800)+800\sqrt{181}}{2*-6000}=\frac{800+800\sqrt{181}}{-12000}
$