7t^2+12t+1=0

Solution for 7t^2+12t+1=0 equation:

Simplifying
7t2 + 12t + 1 = 0

Reorder the terms:
1 + 12t + 7t2 = 0

Solving
1 + 12t + 7t2 = 0

Solving for variable 't'.

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

Divide each side by '7'.
0.1428571429 + 1.714285714t + t2 = 0

Move the constant term to the right:

Add '-0.1428571429' to each side of the equation.
0.1428571429 + 1.714285714t + -0.1428571429 + t2 = 0 + -0.1428571429

Reorder the terms:
0.1428571429 + -0.1428571429 + 1.714285714t + t2 = 0 + -0.1428571429

Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000
0.0000000000 + 1.714285714t + t2 = 0 + -0.1428571429
1.714285714t + t2 = 0 + -0.1428571429

Combine like terms: 0 + -0.1428571429 = -0.1428571429
1.714285714t + t2 = -0.1428571429

The t term is 1.714285714t.  Take half its coefficient (0.857142857).
Square it (0.7346938773) and add it to both sides.

Add '0.7346938773' to each side of the equation.
1.714285714t + 0.7346938773 + t2 = -0.1428571429 + 0.7346938773

Reorder the terms:
0.7346938773 + 1.714285714t + t2 = -0.1428571429 + 0.7346938773

Combine like terms: -0.1428571429 + 0.7346938773 = 0.5918367344
0.7346938773 + 1.714285714t + t2 = 0.5918367344

Factor a perfect square on the left side:
(t + 0.857142857)(t + 0.857142857) = 0.5918367344

Calculate the square root of the right side: 0.769309258

Break this problem into two subproblems by setting 
(t + 0.857142857) equal to 0.769309258 and -0.769309258.

Subproblem 1
t + 0.857142857 = 0.769309258

Simplifying
t + 0.857142857 = 0.769309258

Reorder the terms:
0.857142857 + t = 0.769309258

Solving
0.857142857 + t = 0.769309258

Solving for variable 't'.

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

Add '-0.857142857' to each side of the equation.
0.857142857 + -0.857142857 + t = 0.769309258 + -0.857142857

Combine like terms: 0.857142857 + -0.857142857 = 0.000000000
0.000000000 + t = 0.769309258 + -0.857142857
t = 0.769309258 + -0.857142857

Combine like terms: 0.769309258 + -0.857142857 = -0.087833599
t = -0.087833599

Simplifying
t = -0.087833599

Subproblem 2
t + 0.857142857 = -0.769309258

Simplifying
t + 0.857142857 = -0.769309258

Reorder the terms:
0.857142857 + t = -0.769309258

Solving
0.857142857 + t = -0.769309258

Solving for variable 't'.

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

Add '-0.857142857' to each side of the equation.
0.857142857 + -0.857142857 + t = -0.769309258 + -0.857142857

Combine like terms: 0.857142857 + -0.857142857 = 0.000000000
0.000000000 + t = -0.769309258 + -0.857142857
t = -0.769309258 + -0.857142857

Combine like terms: -0.769309258 + -0.857142857 = -1.626452115
t = -1.626452115

Simplifying
t = -1.626452115

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.087833599, -1.626452115}