0=4.9t^2+30.5t+9.5

Solution for 0=4.9t^2+30.5t+9.5 equation:

0=4.9t^2+30.5t+9.5

We move all terms to the left:

0-(4.9t^2+30.5t+9.5)=0

We add all the numbers together, and all the variables

-(4.9t^2+30.5t+9.5)=0

We get rid of parentheses

-4.9t^2-30.5t-9.5=0

a = -4.9; b = -30.5; c = -9.5;
Δ = b2-4ac
Δ = -30.52-4·(-4.9)·(-9.5)
Δ = 744.05
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{744.05}}{2*-4.9}=\frac{30.5-\sqrt{744.05}}{-9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30.5)+\sqrt{744.05}}{2*-4.9}=\frac{30.5+\sqrt{744.05}}{-9.8}
$