4.9t^2-10.5t-27.3=0

Solution for 4.9t^2-10.5t-27.3=0 equation:

Simplifying
4.9t2 + -10.5t + -27.3 = 0

Reorder the terms:
-27.3 + -10.5t + 4.9t2 = 0

Solving
-27.3 + -10.5t + 4.9t2 = 0

Solving for variable 't'.

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

Divide each side by '4.9'.
-5.571428571 + -2.142857143t + t2 = 0

Move the constant term to the right:

Add '5.571428571' to each side of the equation.
-5.571428571 + -2.142857143t + 5.571428571 + t2 = 0 + 5.571428571

Reorder the terms:
-5.571428571 + 5.571428571 + -2.142857143t + t2 = 0 + 5.571428571

Combine like terms: -5.571428571 + 5.571428571 = 0.000000000
0.000000000 + -2.142857143t + t2 = 0 + 5.571428571
-2.142857143t + t2 = 0 + 5.571428571

Combine like terms: 0 + 5.571428571 = 5.571428571
-2.142857143t + t2 = 5.571428571

The t term is -2.142857143t.  Take half its coefficient (-1.071428572).
Square it (1.147959185) and add it to both sides.

Add '1.147959185' to each side of the equation.
-2.142857143t + 1.147959185 + t2 = 5.571428571 + 1.147959185

Reorder the terms:
1.147959185 + -2.142857143t + t2 = 5.571428571 + 1.147959185

Combine like terms: 5.571428571 + 1.147959185 = 6.719387756
1.147959185 + -2.142857143t + t2 = 6.719387756

Factor a perfect square on the left side:
(t + -1.071428572)(t + -1.071428572) = 6.719387756

Calculate the square root of the right side: 2.592178188

Break this problem into two subproblems by setting 
(t + -1.071428572) equal to 2.592178188 and -2.592178188.

Subproblem 1
t + -1.071428572 = 2.592178188

Simplifying
t + -1.071428572 = 2.592178188

Reorder the terms:
-1.071428572 + t = 2.592178188

Solving
-1.071428572 + t = 2.592178188

Solving for variable 't'.

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

Add '1.071428572' to each side of the equation.
-1.071428572 + 1.071428572 + t = 2.592178188 + 1.071428572

Combine like terms: -1.071428572 + 1.071428572 = 0.000000000
0.000000000 + t = 2.592178188 + 1.071428572
t = 2.592178188 + 1.071428572

Combine like terms: 2.592178188 + 1.071428572 = 3.66360676
t = 3.66360676

Simplifying
t = 3.66360676

Subproblem 2
t + -1.071428572 = -2.592178188

Simplifying
t + -1.071428572 = -2.592178188

Reorder the terms:
-1.071428572 + t = -2.592178188

Solving
-1.071428572 + t = -2.592178188

Solving for variable 't'.

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

Add '1.071428572' to each side of the equation.
-1.071428572 + 1.071428572 + t = -2.592178188 + 1.071428572

Combine like terms: -1.071428572 + 1.071428572 = 0.000000000
0.000000000 + t = -2.592178188 + 1.071428572
t = -2.592178188 + 1.071428572

Combine like terms: -2.592178188 + 1.071428572 = -1.520749616
t = -1.520749616

Simplifying
t = -1.520749616

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.66360676, -1.520749616}