9.8t^2-100t-200=0

Solution for 9.8t^2-100t-200=0 equation:

9.8t^2-100t-200=0

a = 9.8; b = -100; c = -200;
Δ = b2-4ac
Δ = -1002-4·9.8·(-200)
Δ = 17840
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:

$\sqrt{\Delta}=\sqrt{17840}=\sqrt{16*1115}=\sqrt{16}*\sqrt{1115}=4\sqrt{1115}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-4\sqrt{1115}}{2*9.8}=\frac{100-4\sqrt{1115}}{19.6}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+4\sqrt{1115}}{2*9.8}=\frac{100+4\sqrt{1115}}{19.6}
$