39.2=-9.8t+4.9t^2

Solution for 39.2=-9.8t+4.9t^2 equation:

39.2=-9.8t+4.9t^2

We move all terms to the left:

39.2-(-9.8t+4.9t^2)=0

We get rid of parentheses

-4.9t^2+9.8t+39.2=0

a = -4.9; b = 9.8; c = +39.2;
Δ = b2-4ac
Δ = 9.82-4·(-4.9)·39.2
Δ = 864.36
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{864.36}}{2*-4.9}=\frac{-9.8-\sqrt{864.36}}{-9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9.8)+\sqrt{864.36}}{2*-4.9}=\frac{-9.8+\sqrt{864.36}}{-9.8}
$