9.8t^2+30t-6=0

Solution for 9.8t^2+30t-6=0 equation:

Simplifying
9.8t2 + 30t + -6 = 0

Reorder the terms:
-6 + 30t + 9.8t2 = 0

Solving
-6 + 30t + 9.8t2 = 0

Solving for variable 't'.

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

Divide each side by '9.8'.
-0.612244898 + 3.06122449t + t2 = 0

Move the constant term to the right:

Add '0.612244898' to each side of the equation.
-0.612244898 + 3.06122449t + 0.612244898 + t2 = 0 + 0.612244898

Reorder the terms:
-0.612244898 + 0.612244898 + 3.06122449t + t2 = 0 + 0.612244898

Combine like terms: -0.612244898 + 0.612244898 = 0.000000000
0.000000000 + 3.06122449t + t2 = 0 + 0.612244898
3.06122449t + t2 = 0 + 0.612244898

Combine like terms: 0 + 0.612244898 = 0.612244898
3.06122449t + t2 = 0.612244898

The t term is 3.06122449t.  Take half its coefficient (1.530612245).
Square it (2.342773845) and add it to both sides.

Add '2.342773845' to each side of the equation.
3.06122449t + 2.342773845 + t2 = 0.612244898 + 2.342773845

Reorder the terms:
2.342773845 + 3.06122449t + t2 = 0.612244898 + 2.342773845

Combine like terms: 0.612244898 + 2.342773845 = 2.955018743
2.342773845 + 3.06122449t + t2 = 2.955018743

Factor a perfect square on the left side:
(t + 1.530612245)(t + 1.530612245) = 2.955018743

Calculate the square root of the right side: 1.719016795

Break this problem into two subproblems by setting 
(t + 1.530612245) equal to 1.719016795 and -1.719016795.

Subproblem 1
t + 1.530612245 = 1.719016795

Simplifying
t + 1.530612245 = 1.719016795

Reorder the terms:
1.530612245 + t = 1.719016795

Solving
1.530612245 + t = 1.719016795

Solving for variable 't'.

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

Add '-1.530612245' to each side of the equation.
1.530612245 + -1.530612245 + t = 1.719016795 + -1.530612245

Combine like terms: 1.530612245 + -1.530612245 = 0.000000000
0.000000000 + t = 1.719016795 + -1.530612245
t = 1.719016795 + -1.530612245

Combine like terms: 1.719016795 + -1.530612245 = 0.18840455
t = 0.18840455

Simplifying
t = 0.18840455

Subproblem 2
t + 1.530612245 = -1.719016795

Simplifying
t + 1.530612245 = -1.719016795

Reorder the terms:
1.530612245 + t = -1.719016795

Solving
1.530612245 + t = -1.719016795

Solving for variable 't'.

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

Add '-1.530612245' to each side of the equation.
1.530612245 + -1.530612245 + t = -1.719016795 + -1.530612245

Combine like terms: 1.530612245 + -1.530612245 = 0.000000000
0.000000000 + t = -1.719016795 + -1.530612245
t = -1.719016795 + -1.530612245

Combine like terms: -1.719016795 + -1.530612245 = -3.24962904
t = -3.24962904

Simplifying
t = -3.24962904

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.18840455, -3.24962904}