-4.9t^2+30.5t+9.7=0

Solution for -4.9t^2+30.5t+9.7=0 equation:

-4.9t^2+30.5t+9.7=0

a = -4.9; b = 30.5; c = +9.7;
Δ = b2-4ac
Δ = 30.52-4·(-4.9)·9.7
Δ = 1120.37
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{-(30.5)-\sqrt{1120.37}}{2*-4.9}=\frac{-30.5-\sqrt{1120.37}}{-9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30.5)+\sqrt{1120.37}}{2*-4.9}=\frac{-30.5+\sqrt{1120.37}}{-9.8}
$