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

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

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

We move all terms to the left:

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

We get rid of parentheses

4.9t^2-39.2t+t=0

We add all the numbers together, and all the variables

4.9t^2-38.2t=0

a = 4.9; b = -38.2; c = 0;
Δ = b2-4ac
Δ = -38.22-4·4.9·0
Δ = 1459.24
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{-(-38.2)-\sqrt{1459.24}}{2*4.9}=\frac{38.2-\sqrt{1459.24}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38.2)+\sqrt{1459.24}}{2*4.9}=\frac{38.2+\sqrt{1459.24}}{9.8}
$