4t^2+12t-1=0

Solution for 4t^2+12t-1=0 equation:

Simplifying
4t2 + 12t + -1 = 0

Reorder the terms:
-1 + 12t + 4t2 = 0

Solving
-1 + 12t + 4t2 = 0

Solving for variable 't'.

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

Divide each side by '4'.
-0.25 + 3t + t2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + 3t + 0.25 + t2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + 3t + t2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + 3t + t2 = 0 + 0.25
3t + t2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
3t + t2 = 0.25

The t term is 3t.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3t + 2.25 + t2 = 0.25 + 2.25

Reorder the terms:
2.25 + 3t + t2 = 0.25 + 2.25

Combine like terms: 0.25 + 2.25 = 2.5
2.25 + 3t + t2 = 2.5

Factor a perfect square on the left side:
(t + 1.5)(t + 1.5) = 2.5

Calculate the square root of the right side: 1.58113883

Break this problem into two subproblems by setting 
(t + 1.5) equal to 1.58113883 and -1.58113883.

Subproblem 1
t + 1.5 = 1.58113883

Simplifying
t + 1.5 = 1.58113883

Reorder the terms:
1.5 + t = 1.58113883

Solving
1.5 + t = 1.58113883

Solving for variable 't'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + t = 1.58113883 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + t = 1.58113883 + -1.5
t = 1.58113883 + -1.5

Combine like terms: 1.58113883 + -1.5 = 0.08113883
t = 0.08113883

Simplifying
t = 0.08113883

Subproblem 2
t + 1.5 = -1.58113883

Simplifying
t + 1.5 = -1.58113883

Reorder the terms:
1.5 + t = -1.58113883

Solving
1.5 + t = -1.58113883

Solving for variable 't'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + t = -1.58113883 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + t = -1.58113883 + -1.5
t = -1.58113883 + -1.5

Combine like terms: -1.58113883 + -1.5 = -3.08113883
t = -3.08113883

Simplifying
t = -3.08113883

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.08113883, -3.08113883}