39.2=-4.9(t)^2+29.4t

Solution for 39.2=-4.9(t)^2+29.4t equation:

39.2=-4.9(t)^2+29.4t

We move all terms to the left:

39.2-(-4.9(t)^2+29.4t)=0

We get rid of parentheses

4.9t^2-29.4t+39.2=0

a = 4.9; b = -29.4; c = +39.2;
Δ = b2-4ac
Δ = -29.42-4·4.9·39.2
Δ = 96.04
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{-(-29.4)-\sqrt{96.04}}{2*4.9}=\frac{29.4-\sqrt{96.04}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29.4)+\sqrt{96.04}}{2*4.9}=\frac{29.4+\sqrt{96.04}}{9.8}
$