1.5t2-50t-500=0

Solution for 1.5t2-50t-500=0 equation:

1.5t^2-50t-500=0

a = 1.5; b = -50; c = -500;
Δ = b2-4ac
Δ = -502-4·1.5·(-500)
Δ = 5500
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:

$\sqrt{\Delta}=\sqrt{5500}=\sqrt{100*55}=\sqrt{100}*\sqrt{55}=10\sqrt{55}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-10\sqrt{55}}{2*1.5}=\frac{50-10\sqrt{55}}{3}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+10\sqrt{55}}{2*1.5}=\frac{50+10\sqrt{55}}{3}
$