.583=.5*9.8*t^2

Solution for .583=.5*9.8*t^2 equation:

Simplifying
0.583 = 0.5 * 9.8t2

Multiply 0.5 * 9.8
0.583 = 4.9t2

Solving
0.583 = 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.
0.583 + -4.9t2 = 4.9t2 + -4.9t2

Combine like terms: 4.9t2 + -4.9t2 = 0.0
0.583 + -4.9t2 = 0.0

Add '-0.583' to each side of the equation.
0.583 + -0.583 + -4.9t2 = 0.0 + -0.583

Combine like terms: 0.583 + -0.583 = 0.000
0.000 + -4.9t2 = 0.0 + -0.583
-4.9t2 = 0.0 + -0.583

Combine like terms: 0.0 + -0.583 = -0.583
-4.9t2 = -0.583

Divide each side by '-4.9'.
t2 = 0.1189795918

Simplifying
t2 = 0.1189795918

Take the square root of each side:
t = {-0.344934185, 0.344934185}