0=72+13.5t-4.9t^2

Solution for 0=72+13.5t-4.9t^2 equation:

0=72+13.5t-4.9t^2

We move all terms to the left:

0-(72+13.5t-4.9t^2)=0

We add all the numbers together, and all the variables

-(72+13.5t-4.9t^2)=0

We get rid of parentheses

4.9t^2-13.5t-72=0

a = 4.9; b = -13.5; c = -72;
Δ = b2-4ac
Δ = -13.52-4·4.9·(-72)
Δ = 1593.45
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{-(-13.5)-\sqrt{1593.45}}{2*4.9}=\frac{13.5-\sqrt{1593.45}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13.5)+\sqrt{1593.45}}{2*4.9}=\frac{13.5+\sqrt{1593.45}}{9.8}
$