-4.9t^2+24.5t+8.6=0

Solution for -4.9t^2+24.5t+8.6=0 equation:

-4.9t^2+24.5t+8.6=0

a = -4.9; b = 24.5; c = +8.6;
Δ = b2-4ac
Δ = 24.52-4·(-4.9)·8.6
Δ = 768.81
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{-(24.5)-\sqrt{768.81}}{2*-4.9}=\frac{-24.5-\sqrt{768.81}}{-9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24.5)+\sqrt{768.81}}{2*-4.9}=\frac{-24.5+\sqrt{768.81}}{-9.8}
$