16t^2-250t-500=0

Solution for 16t^2-250t-500=0 equation:

16t^2-250t-500=0

a = 16; b = -250; c = -500;
Δ = b2-4ac
Δ = -2502-4·16·(-500)
Δ = 94500
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:

$\sqrt{\Delta}=\sqrt{94500}=\sqrt{900*105}=\sqrt{900}*\sqrt{105}=30\sqrt{105}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-250)-30\sqrt{105}}{2*16}=\frac{250-30\sqrt{105}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-250)+30\sqrt{105}}{2*16}=\frac{250+30\sqrt{105}}{32}
$