50t^2+100t-130=0

Solution for 50t^2+100t-130=0 equation:

Simplifying
50t2 + 100t + -130 = 0

Reorder the terms:
-130 + 100t + 50t2 = 0

Solving
-130 + 100t + 50t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '10'.
10(-13 + 10t + 5t2) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(-13 + 10t + 5t2)' equal to zero and attempt to solve:

Simplifying
-13 + 10t + 5t2 = 0

Solving
-13 + 10t + 5t2 = 0

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

Divide each side by '5'.
-2.6 + 2t + t2 = 0

Move the constant term to the right:

Add '2.6' to each side of the equation.
-2.6 + 2t + 2.6 + t2 = 0 + 2.6

Reorder the terms:
-2.6 + 2.6 + 2t + t2 = 0 + 2.6

Combine like terms: -2.6 + 2.6 = 0.0
0.0 + 2t + t2 = 0 + 2.6
2t + t2 = 0 + 2.6

Combine like terms: 0 + 2.6 = 2.6
2t + t2 = 2.6

The t term is 2t.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2t + 1 + t2 = 2.6 + 1

Reorder the terms:
1 + 2t + t2 = 2.6 + 1

Combine like terms: 2.6 + 1 = 3.6
1 + 2t + t2 = 3.6

Factor a perfect square on the left side:
(t + 1)(t + 1) = 3.6

Calculate the square root of the right side: 1.897366596

Break this problem into two subproblems by setting 
(t + 1) equal to 1.897366596 and -1.897366596.

Subproblem 1
t + 1 = 1.897366596

Simplifying
t + 1 = 1.897366596

Reorder the terms:
1 + t = 1.897366596

Solving
1 + t = 1.897366596

Solving for variable 't'.

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

Add '-1' to each side of the equation.
1 + -1 + t = 1.897366596 + -1

Combine like terms: 1 + -1 = 0
0 + t = 1.897366596 + -1
t = 1.897366596 + -1

Combine like terms: 1.897366596 + -1 = 0.897366596
t = 0.897366596

Simplifying
t = 0.897366596

Subproblem 2
t + 1 = -1.897366596

Simplifying
t + 1 = -1.897366596

Reorder the terms:
1 + t = -1.897366596

Solving
1 + t = -1.897366596

Solving for variable 't'.

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

Add '-1' to each side of the equation.
1 + -1 + t = -1.897366596 + -1

Combine like terms: 1 + -1 = 0
0 + t = -1.897366596 + -1
t = -1.897366596 + -1

Combine like terms: -1.897366596 + -1 = -2.897366596
t = -2.897366596

Simplifying
t = -2.897366596

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.897366596, -2.897366596}
Solution
t = {0.897366596, -2.897366596}