-4.9t^2-9.8t+73.5=0

Solution for -4.9t^2-9.8t+73.5=0 equation:

-4.9t^2-9.8t+73.5=0

a = -4.9; b = -9.8; c = +73.5;
Δ = b2-4ac
Δ = -9.82-4·(-4.9)·73.5
Δ = 1536.64
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{-(-9.8)-\sqrt{1536.64}}{2*-4.9}=\frac{9.8-\sqrt{1536.64}}{-9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9.8)+\sqrt{1536.64}}{2*-4.9}=\frac{9.8+\sqrt{1536.64}}{-9.8}
$