.680=.5*9.8*t^2

Solution for .680=.5*9.8*t^2 equation:

Simplifying
0.680 = 0.5 * 9.8t2

Multiply 0.5 * 9.8
0.680 = 4.9t2

Solving
0.680 = 4.9t2

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '-4.9t2' to each side of the equation.
0.680 + -4.9t2 = 4.9t2 + -4.9t2

Combine like terms: 4.9t2 + -4.9t2 = 0.0
0.680 + -4.9t2 = 0.0

Add '-0.680' to each side of the equation.
0.680 + -0.680 + -4.9t2 = 0.0 + -0.680

Combine like terms: 0.680 + -0.680 = 0.000
0.000 + -4.9t2 = 0.0 + -0.680
-4.9t2 = 0.0 + -0.680

Combine like terms: 0.0 + -0.680 = -0.68
-4.9t2 = -0.68

Divide each side by '-4.9'.
t2 = 0.1387755102

Simplifying
t2 = 0.1387755102

Take the square root of each side:
t = {-0.372525852, 0.372525852}