-9.8t(.5t+1)+39.2=0

Solution for -9.8t(.5t+1)+39.2=0 equation:

-9.8t(.5t+1)+39.2=0

We multiply parentheses

-9t^2-9t+39.2=0

a = -9; b = -9; c = +39.2;
Δ = b2-4ac
Δ = -92-4·(-9)·39.2
Δ = 1492.2
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)-\sqrt{1492.2}}{2*-9}=\frac{9-\sqrt{1492.2}}{-18}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{1492.2}}{2*-9}=\frac{9+\sqrt{1492.2}}{-18}
$