1.5t2-50t-25000=0

Solution for 1.5t2-50t-25000=0 equation:

1.5t^2-50t-25000=0

a = 1.5; b = -50; c = -25000;
Δ = b2-4ac
Δ = -502-4·1.5·(-25000)
Δ = 152500
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:

$\sqrt{\Delta}=\sqrt{152500}=\sqrt{2500*61}=\sqrt{2500}*\sqrt{61}=50\sqrt{61}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-50\sqrt{61}}{2*1.5}=\frac{50-50\sqrt{61}}{3}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+50\sqrt{61}}{2*1.5}=\frac{50+50\sqrt{61}}{3}
$