50t^2+100t=2120

Solution for 50t^2+100t=2120 equation:

Simplifying
50t2 + 100t = 2120

Reorder the terms:
100t + 50t2 = 2120

Solving
100t + 50t2 = 2120

Solving for variable 't'.

Reorder the terms:
-2120 + 100t + 50t2 = 2120 + -2120

Combine like terms: 2120 + -2120 = 0
-2120 + 100t + 50t2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(-212 + 10t + 5t2) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(-212 + 10t + 5t2)' equal to zero and attempt to solve:

Simplifying
-212 + 10t + 5t2 = 0

Solving
-212 + 10t + 5t2 = 0

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

Divide each side by '5'.
-42.4 + 2t + t2 = 0

Move the constant term to the right:

Add '42.4' to each side of the equation.
-42.4 + 2t + 42.4 + t2 = 0 + 42.4

Reorder the terms:
-42.4 + 42.4 + 2t + t2 = 0 + 42.4

Combine like terms: -42.4 + 42.4 = 0.0
0.0 + 2t + t2 = 0 + 42.4
2t + t2 = 0 + 42.4

Combine like terms: 0 + 42.4 = 42.4
2t + t2 = 42.4

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 = 42.4 + 1

Reorder the terms:
1 + 2t + t2 = 42.4 + 1

Combine like terms: 42.4 + 1 = 43.4
1 + 2t + t2 = 43.4

Factor a perfect square on the left side:
(t + 1)(t + 1) = 43.4

Calculate the square root of the right side: 6.587867637

Break this problem into two subproblems by setting 
(t + 1) equal to 6.587867637 and -6.587867637.

Subproblem 1
t + 1 = 6.587867637

Simplifying
t + 1 = 6.587867637

Reorder the terms:
1 + t = 6.587867637

Solving
1 + t = 6.587867637

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 = 6.587867637 + -1

Combine like terms: 1 + -1 = 0
0 + t = 6.587867637 + -1
t = 6.587867637 + -1

Combine like terms: 6.587867637 + -1 = 5.587867637
t = 5.587867637

Simplifying
t = 5.587867637

Subproblem 2
t + 1 = -6.587867637

Simplifying
t + 1 = -6.587867637

Reorder the terms:
1 + t = -6.587867637

Solving
1 + t = -6.587867637

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 = -6.587867637 + -1

Combine like terms: 1 + -1 = 0
0 + t = -6.587867637 + -1
t = -6.587867637 + -1

Combine like terms: -6.587867637 + -1 = -7.587867637
t = -7.587867637

Simplifying
t = -7.587867637

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {5.587867637, -7.587867637}
Solution
t = {5.587867637, -7.587867637}