6.2t^2+12t+32=120

Solution for 6.2t^2+12t+32=120 equation:

Simplifying
6.2t2 + 12t + 32 = 120

Reorder the terms:
32 + 12t + 6.2t2 = 120

Solving
32 + 12t + 6.2t2 = 120

Solving for variable 't'.

Reorder the terms:
32 + -120 + 12t + 6.2t2 = 120 + -120

Combine like terms: 32 + -120 = -88
-88 + 12t + 6.2t2 = 120 + -120

Combine like terms: 120 + -120 = 0
-88 + 12t + 6.2t2 = 0

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

Divide each side by '6.2'.
-14.19354839 + 1.935483871t + t2 = 0

Move the constant term to the right:

Add '14.19354839' to each side of the equation.
-14.19354839 + 1.935483871t + 14.19354839 + t2 = 0 + 14.19354839

Reorder the terms:
-14.19354839 + 14.19354839 + 1.935483871t + t2 = 0 + 14.19354839

Combine like terms: -14.19354839 + 14.19354839 = 0.00000000
0.00000000 + 1.935483871t + t2 = 0 + 14.19354839
1.935483871t + t2 = 0 + 14.19354839

Combine like terms: 0 + 14.19354839 = 14.19354839
1.935483871t + t2 = 14.19354839

The t term is 1.935483871t.  Take half its coefficient (0.9677419355).
Square it (0.9365244537) and add it to both sides.

Add '0.9365244537' to each side of the equation.
1.935483871t + 0.9365244537 + t2 = 14.19354839 + 0.9365244537

Reorder the terms:
0.9365244537 + 1.935483871t + t2 = 14.19354839 + 0.9365244537

Combine like terms: 14.19354839 + 0.9365244537 = 15.1300728437
0.9365244537 + 1.935483871t + t2 = 15.1300728437

Factor a perfect square on the left side:
(t + 0.9677419355)(t + 0.9677419355) = 15.1300728437

Calculate the square root of the right side: 3.889739431

Break this problem into two subproblems by setting 
(t + 0.9677419355) equal to 3.889739431 and -3.889739431.

Subproblem 1
t + 0.9677419355 = 3.889739431

Simplifying
t + 0.9677419355 = 3.889739431

Reorder the terms:
0.9677419355 + t = 3.889739431

Solving
0.9677419355 + t = 3.889739431

Solving for variable 't'.

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

Add '-0.9677419355' to each side of the equation.
0.9677419355 + -0.9677419355 + t = 3.889739431 + -0.9677419355

Combine like terms: 0.9677419355 + -0.9677419355 = 0.0000000000
0.0000000000 + t = 3.889739431 + -0.9677419355
t = 3.889739431 + -0.9677419355

Combine like terms: 3.889739431 + -0.9677419355 = 2.9219974955
t = 2.9219974955

Simplifying
t = 2.9219974955

Subproblem 2
t + 0.9677419355 = -3.889739431

Simplifying
t + 0.9677419355 = -3.889739431

Reorder the terms:
0.9677419355 + t = -3.889739431

Solving
0.9677419355 + t = -3.889739431

Solving for variable 't'.

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

Add '-0.9677419355' to each side of the equation.
0.9677419355 + -0.9677419355 + t = -3.889739431 + -0.9677419355

Combine like terms: 0.9677419355 + -0.9677419355 = 0.0000000000
0.0000000000 + t = -3.889739431 + -0.9677419355
t = -3.889739431 + -0.9677419355

Combine like terms: -3.889739431 + -0.9677419355 = -4.8574813665
t = -4.8574813665

Simplifying
t = -4.8574813665

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.9219974955, -4.8574813665}