0=-4t^2+30.5t+9.6

Solution for 0=-4t^2+30.5t+9.6 equation:

0=-4t^2+30.5t+9.6

We move all terms to the left:

0-(-4t^2+30.5t+9.6)=0

We add all the numbers together, and all the variables

-(-4t^2+30.5t+9.6)=0

We get rid of parentheses

4t^2-30.5t-9.6=0

a = 4; b = -30.5; c = -9.6;
Δ = b2-4ac
Δ = -30.52-4·4·(-9.6)
Δ = 1083.85
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{1083.85}}{2*4}=\frac{30.5-\sqrt{1083.85}}{8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30.5)+\sqrt{1083.85}}{2*4}=\frac{30.5+\sqrt{1083.85}}{8}
$