0=-33.4+30t^2-4.9t

Solution for 0=-33.4+30t^2-4.9t equation:

Simplifying
0 = -33.4 + 30t2 + -4.9t

Reorder the terms:
0 = -33.4 + -4.9t + 30t2

Solving
0 = -33.4 + -4.9t + 30t2

Solving for variable 't'.

Combine like terms: 0 + 33.4 = 33.4
33.4 + 4.9t + -30t2 = -33.4 + -4.9t + 30t2 + 33.4 + 4.9t + -30t2

Reorder the terms:
33.4 + 4.9t + -30t2 = -33.4 + 33.4 + -4.9t + 4.9t + 30t2 + -30t2

Combine like terms: -33.4 + 33.4 = 0.0
33.4 + 4.9t + -30t2 = 0.0 + -4.9t + 4.9t + 30t2 + -30t2
33.4 + 4.9t + -30t2 = -4.9t + 4.9t + 30t2 + -30t2

Combine like terms: -4.9t + 4.9t = 0.0
33.4 + 4.9t + -30t2 = 0.0 + 30t2 + -30t2
33.4 + 4.9t + -30t2 = 30t2 + -30t2

Combine like terms: 30t2 + -30t2 = 0
33.4 + 4.9t + -30t2 = 0

Begin completing the square.  Divide all terms by
-30 the coefficient of the squared term: 

Divide each side by '-30'.
-1.113333333 + -0.1633333333t + t2 = 0

Move the constant term to the right:

Add '1.113333333' to each side of the equation.
-1.113333333 + -0.1633333333t + 1.113333333 + t2 = 0 + 1.113333333

Reorder the terms:
-1.113333333 + 1.113333333 + -0.1633333333t + t2 = 0 + 1.113333333

Combine like terms: -1.113333333 + 1.113333333 = 0.000000000
0.000000000 + -0.1633333333t + t2 = 0 + 1.113333333
-0.1633333333t + t2 = 0 + 1.113333333

Combine like terms: 0 + 1.113333333 = 1.113333333
-0.1633333333t + t2 = 1.113333333

The t term is -0.1633333333t.  Take half its coefficient (-0.08166666665).
Square it (0.006669444442) and add it to both sides.

Add '0.006669444442' to each side of the equation.
-0.1633333333t + 0.006669444442 + t2 = 1.113333333 + 0.006669444442

Reorder the terms:
0.006669444442 + -0.1633333333t + t2 = 1.113333333 + 0.006669444442

Combine like terms: 1.113333333 + 0.006669444442 = 1.120002777442
0.006669444442 + -0.1633333333t + t2 = 1.120002777442

Factor a perfect square on the left side:
(t + -0.08166666665)(t + -0.08166666665) = 1.120002777442

Calculate the square root of the right side: 1.058301837

Break this problem into two subproblems by setting 
(t + -0.08166666665) equal to 1.058301837 and -1.058301837.

Subproblem 1
t + -0.08166666665 = 1.058301837

Simplifying
t + -0.08166666665 = 1.058301837

Reorder the terms:
-0.08166666665 + t = 1.058301837

Solving
-0.08166666665 + t = 1.058301837

Solving for variable 't'.

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

Add '0.08166666665' to each side of the equation.
-0.08166666665 + 0.08166666665 + t = 1.058301837 + 0.08166666665

Combine like terms: -0.08166666665 + 0.08166666665 = 0.00000000000
0.00000000000 + t = 1.058301837 + 0.08166666665
t = 1.058301837 + 0.08166666665

Combine like terms: 1.058301837 + 0.08166666665 = 1.13996850365
t = 1.13996850365

Simplifying
t = 1.13996850365

Subproblem 2
t + -0.08166666665 = -1.058301837

Simplifying
t + -0.08166666665 = -1.058301837

Reorder the terms:
-0.08166666665 + t = -1.058301837

Solving
-0.08166666665 + t = -1.058301837

Solving for variable 't'.

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

Add '0.08166666665' to each side of the equation.
-0.08166666665 + 0.08166666665 + t = -1.058301837 + 0.08166666665

Combine like terms: -0.08166666665 + 0.08166666665 = 0.00000000000
0.00000000000 + t = -1.058301837 + 0.08166666665
t = -1.058301837 + 0.08166666665

Combine like terms: -1.058301837 + 0.08166666665 = -0.97663517035
t = -0.97663517035

Simplifying
t = -0.97663517035

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.13996850365, -0.97663517035}