-5t^2-240t-1734=0

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Solution for -5t^2-240t-1734=0 equation: 


Simplifying
-5t2 + -240t + -1734 = 0

Reorder the terms:
-1734 + -240t + -5t2 = 0

Solving
-1734 + -240t + -5t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1734 + 240t + 5t2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(1734 + 240t + 5t2)' equal to zero and attempt to solve:

Simplifying
1734 + 240t + 5t2 = 0

Solving
1734 + 240t + 5t2 = 0

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

Divide each side by '5'.
346.8 + 48t + t2 = 0

Move the constant term to the right:

Add '-346.8' to each side of the equation.
346.8 + 48t + -346.8 + t2 = 0 + -346.8

Reorder the terms:
346.8 + -346.8 + 48t + t2 = 0 + -346.8

Combine like terms: 346.8 + -346.8 = 0.0
0.0 + 48t + t2 = 0 + -346.8
48t + t2 = 0 + -346.8

Combine like terms: 0 + -346.8 = -346.8
48t + t2 = -346.8

The t term is 48t.  Take half its coefficient (24).
Square it (576) and add it to both sides.

Add '576' to each side of the equation.
48t + 576 + t2 = -346.8 + 576

Reorder the terms:
576 + 48t + t2 = -346.8 + 576

Combine like terms: -346.8 + 576 = 229.2
576 + 48t + t2 = 229.2

Factor a perfect square on the left side:
(t + 24)(t + 24) = 229.2

Calculate the square root of the right side: 15.139352694

Break this problem into two subproblems by setting 
(t + 24) equal to 15.139352694 and -15.139352694.


Subproblem 1
t + 24 = 15.139352694

Simplifying
t + 24 = 15.139352694

Reorder the terms:
24 + t = 15.139352694

Solving
24 + t = 15.139352694

Solving for variable 't'.

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

Add '-24' to each side of the equation.
24 + -24 + t = 15.139352694 + -24

Combine like terms: 24 + -24 = 0
0 + t = 15.139352694 + -24
t = 15.139352694 + -24

Combine like terms: 15.139352694 + -24 = -8.860647306
t = -8.860647306

Simplifying
t = -8.860647306


Subproblem 2
t + 24 = -15.139352694

Simplifying
t + 24 = -15.139352694

Reorder the terms:
24 + t = -15.139352694

Solving
24 + t = -15.139352694

Solving for variable 't'.

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

Add '-24' to each side of the equation.
24 + -24 + t = -15.139352694 + -24

Combine like terms: 24 + -24 = 0
0 + t = -15.139352694 + -24
t = -15.139352694 + -24

Combine like terms: -15.139352694 + -24 = -39.139352694
t = -39.139352694

Simplifying
t = -39.139352694


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-8.860647306, -39.139352694}
Solution
t = {-8.860647306, -39.139352694}

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