50t^2+100t-80=0

Solution for 50t^2+100t-80=0 equation:

Simplifying
50t2 + 100t + -80 = 0

Reorder the terms:
-80 + 100t + 50t2 = 0

Solving
-80 + 100t + 50t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '10'.
10(-8 + 10t + 5t2) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(-8 + 10t + 5t2)' equal to zero and attempt to solve:

Simplifying
-8 + 10t + 5t2 = 0

Solving
-8 + 10t + 5t2 = 0

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

Divide each side by '5'.
-1.6 + 2t + t2 = 0

Move the constant term to the right:

Add '1.6' to each side of the equation.
-1.6 + 2t + 1.6 + t2 = 0 + 1.6

Reorder the terms:
-1.6 + 1.6 + 2t + t2 = 0 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + 2t + t2 = 0 + 1.6
2t + t2 = 0 + 1.6

Combine like terms: 0 + 1.6 = 1.6
2t + t2 = 1.6

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 = 1.6 + 1

Reorder the terms:
1 + 2t + t2 = 1.6 + 1

Combine like terms: 1.6 + 1 = 2.6
1 + 2t + t2 = 2.6

Factor a perfect square on the left side:
(t + 1)(t + 1) = 2.6

Calculate the square root of the right side: 1.61245155

Break this problem into two subproblems by setting 
(t + 1) equal to 1.61245155 and -1.61245155.

Subproblem 1
t + 1 = 1.61245155

Simplifying
t + 1 = 1.61245155

Reorder the terms:
1 + t = 1.61245155

Solving
1 + t = 1.61245155

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 = 1.61245155 + -1

Combine like terms: 1 + -1 = 0
0 + t = 1.61245155 + -1
t = 1.61245155 + -1

Combine like terms: 1.61245155 + -1 = 0.61245155
t = 0.61245155

Simplifying
t = 0.61245155

Subproblem 2
t + 1 = -1.61245155

Simplifying
t + 1 = -1.61245155

Reorder the terms:
1 + t = -1.61245155

Solving
1 + t = -1.61245155

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 = -1.61245155 + -1

Combine like terms: 1 + -1 = 0
0 + t = -1.61245155 + -1
t = -1.61245155 + -1

Combine like terms: -1.61245155 + -1 = -2.61245155
t = -2.61245155

Simplifying
t = -2.61245155

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.61245155, -2.61245155}
Solution
t = {0.61245155, -2.61245155}