1.5t2-50t-10=0

Solution for 1.5t2-50t-10=0 equation:

1.5t^2-50t-10=0

a = 1.5; b = -50; c = -10;
Δ = b2-4ac
Δ = -502-4·1.5·(-10)
Δ = 2560
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:

$\sqrt{\Delta}=\sqrt{2560}=\sqrt{256*10}=\sqrt{256}*\sqrt{10}=16\sqrt{10}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-16\sqrt{10}}{2*1.5}=\frac{50-16\sqrt{10}}{3}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+16\sqrt{10}}{2*1.5}=\frac{50+16\sqrt{10}}{3}
$