-413.8t^2+929.9t-298.9=0

Solution for -413.8t^2+929.9t-298.9=0 equation:

Simplifying
-413.8t2 + 929.9t + -298.9 = 0

Reorder the terms:
-298.9 + 929.9t + -413.8t2 = 0

Solving
-298.9 + 929.9t + -413.8t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
-413.8 the coefficient of the squared term: 

Divide each side by '-413.8'.
0.7223296278 + -2.24722088t + t2 = 0

Move the constant term to the right:

Add '-0.7223296278' to each side of the equation.
0.7223296278 + -2.24722088t + -0.7223296278 + t2 = 0 + -0.7223296278

Reorder the terms:
0.7223296278 + -0.7223296278 + -2.24722088t + t2 = 0 + -0.7223296278

Combine like terms: 0.7223296278 + -0.7223296278 = 0.0000000000
0.0000000000 + -2.24722088t + t2 = 0 + -0.7223296278
-2.24722088t + t2 = 0 + -0.7223296278

Combine like terms: 0 + -0.7223296278 = -0.7223296278
-2.24722088t + t2 = -0.7223296278

The t term is -2.24722088t.  Take half its coefficient (-1.12361044).
Square it (1.262500421) and add it to both sides.

Add '1.262500421' to each side of the equation.
-2.24722088t + 1.262500421 + t2 = -0.7223296278 + 1.262500421

Reorder the terms:
1.262500421 + -2.24722088t + t2 = -0.7223296278 + 1.262500421

Combine like terms: -0.7223296278 + 1.262500421 = 0.5401707932
1.262500421 + -2.24722088t + t2 = 0.5401707932

Factor a perfect square on the left side:
(t + -1.12361044)(t + -1.12361044) = 0.5401707932

Calculate the square root of the right side: 0.734963124

Break this problem into two subproblems by setting 
(t + -1.12361044) equal to 0.734963124 and -0.734963124.

Subproblem 1
t + -1.12361044 = 0.734963124

Simplifying
t + -1.12361044 = 0.734963124

Reorder the terms:
-1.12361044 + t = 0.734963124

Solving
-1.12361044 + t = 0.734963124

Solving for variable 't'.

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

Add '1.12361044' to each side of the equation.
-1.12361044 + 1.12361044 + t = 0.734963124 + 1.12361044

Combine like terms: -1.12361044 + 1.12361044 = 0.00000000
0.00000000 + t = 0.734963124 + 1.12361044
t = 0.734963124 + 1.12361044

Combine like terms: 0.734963124 + 1.12361044 = 1.858573564
t = 1.858573564

Simplifying
t = 1.858573564

Subproblem 2
t + -1.12361044 = -0.734963124

Simplifying
t + -1.12361044 = -0.734963124

Reorder the terms:
-1.12361044 + t = -0.734963124

Solving
-1.12361044 + t = -0.734963124

Solving for variable 't'.

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

Add '1.12361044' to each side of the equation.
-1.12361044 + 1.12361044 + t = -0.734963124 + 1.12361044

Combine like terms: -1.12361044 + 1.12361044 = 0.00000000
0.00000000 + t = -0.734963124 + 1.12361044
t = -0.734963124 + 1.12361044

Combine like terms: -0.734963124 + 1.12361044 = 0.388647316
t = 0.388647316

Simplifying
t = 0.388647316

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.858573564, 0.388647316}