80*t^2-260*t-105=0

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Solution for 80*t^2-260*t-105=0 equation:


Simplifying
80t2 + -260t + -105 = 0

Reorder the terms:
-105 + -260t + 80t2 = 0

Solving
-105 + -260t + 80t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-21 + -52t + 16t2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-21 + -52t + 16t2)' equal to zero and attempt to solve:

Simplifying
-21 + -52t + 16t2 = 0

Solving
-21 + -52t + 16t2 = 0

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

Divide each side by '16'.
-1.3125 + -3.25t + t2 = 0

Move the constant term to the right:

Add '1.3125' to each side of the equation.
-1.3125 + -3.25t + 1.3125 + t2 = 0 + 1.3125

Reorder the terms:
-1.3125 + 1.3125 + -3.25t + t2 = 0 + 1.3125

Combine like terms: -1.3125 + 1.3125 = 0.0000
0.0000 + -3.25t + t2 = 0 + 1.3125
-3.25t + t2 = 0 + 1.3125

Combine like terms: 0 + 1.3125 = 1.3125
-3.25t + t2 = 1.3125

The t term is -3.25t.  Take half its coefficient (-1.625).
Square it (2.640625) and add it to both sides.

Add '2.640625' to each side of the equation.
-3.25t + 2.640625 + t2 = 1.3125 + 2.640625

Reorder the terms:
2.640625 + -3.25t + t2 = 1.3125 + 2.640625

Combine like terms: 1.3125 + 2.640625 = 3.953125
2.640625 + -3.25t + t2 = 3.953125

Factor a perfect square on the left side:
(t + -1.625)(t + -1.625) = 3.953125

Calculate the square root of the right side: 1.988246715

Break this problem into two subproblems by setting 
(t + -1.625) equal to 1.988246715 and -1.988246715.


Subproblem 1
t + -1.625 = 1.988246715

Simplifying
t + -1.625 = 1.988246715

Reorder the terms:
-1.625 + t = 1.988246715

Solving
-1.625 + t = 1.988246715

Solving for variable 't'.

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

Add '1.625' to each side of the equation.
-1.625 + 1.625 + t = 1.988246715 + 1.625

Combine like terms: -1.625 + 1.625 = 0.000
0.000 + t = 1.988246715 + 1.625
t = 1.988246715 + 1.625

Combine like terms: 1.988246715 + 1.625 = 3.613246715
t = 3.613246715

Simplifying
t = 3.613246715


Subproblem 2
t + -1.625 = -1.988246715

Simplifying
t + -1.625 = -1.988246715

Reorder the terms:
-1.625 + t = -1.988246715

Solving
-1.625 + t = -1.988246715

Solving for variable 't'.

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

Add '1.625' to each side of the equation.
-1.625 + 1.625 + t = -1.988246715 + 1.625

Combine like terms: -1.625 + 1.625 = 0.000
0.000 + t = -1.988246715 + 1.625
t = -1.988246715 + 1.625

Combine like terms: -1.988246715 + 1.625 = -0.363246715
t = -0.363246715

Simplifying
t = -0.363246715


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.613246715, -0.363246715}
Solution
t = {3.613246715, -0.363246715}

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