.680=.5*6.91*t^2

Solution for .680=.5*6.91*t^2 equation:

Simplifying
0.680 = 0.5 * 6.91t2

Multiply 0.5 * 6.91
0.680 = 3.455t2

Solving
0.680 = 3.455t2

Solving for variable 't'.

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

Add '-3.455t2' to each side of the equation.
0.680 + -3.455t2 = 3.455t2 + -3.455t2

Combine like terms: 3.455t2 + -3.455t2 = 0.000
0.680 + -3.455t2 = 0.000

Add '-0.680' to each side of the equation.
0.680 + -0.680 + -3.455t2 = 0.000 + -0.680

Combine like terms: 0.680 + -0.680 = 0.000
0.000 + -3.455t2 = 0.000 + -0.680
-3.455t2 = 0.000 + -0.680

Combine like terms: 0.000 + -0.680 = -0.68
-3.455t2 = -0.68

Divide each side by '-3.455'.
t2 = 0.1968162084

Simplifying
t2 = 0.1968162084

Take the square root of each side:
t = {-0.443639728, 0.443639728}