4.9t^2-51.96t-200=0

Solution for 4.9t^2-51.96t-200=0 equation:

4.9t^2-51.96t-200=0

a = 4.9; b = -51.96; c = -200;
Δ = b2-4ac
Δ = -51.962-4·4.9·(-200)
Δ = 6619.8416
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51.96)-\sqrt{6619.8416}}{2*4.9}=\frac{51.96-\sqrt{6619.8416}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51.96)+\sqrt{6619.8416}}{2*4.9}=\frac{51.96+\sqrt{6619.8416}}{9.8}
$