5t^2+12t-1=0

Solution for 5t^2+12t-1=0 equation:

Simplifying
5t2 + 12t + -1 = 0

Reorder the terms:
-1 + 12t + 5t2 = 0

Solving
-1 + 12t + 5t2 = 0

Solving for variable 't'.

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

Divide each side by '5'.
-0.2 + 2.4t + t2 = 0

Move the constant term to the right:

Add '0.2' to each side of the equation.
-0.2 + 2.4t + 0.2 + t2 = 0 + 0.2

Reorder the terms:
-0.2 + 0.2 + 2.4t + t2 = 0 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + 2.4t + t2 = 0 + 0.2
2.4t + t2 = 0 + 0.2

Combine like terms: 0 + 0.2 = 0.2
2.4t + t2 = 0.2

The t term is 2.4t.  Take half its coefficient (1.2).
Square it (1.44) and add it to both sides.

Add '1.44' to each side of the equation.
2.4t + 1.44 + t2 = 0.2 + 1.44

Reorder the terms:
1.44 + 2.4t + t2 = 0.2 + 1.44

Combine like terms: 0.2 + 1.44 = 1.64
1.44 + 2.4t + t2 = 1.64

Factor a perfect square on the left side:
(t + 1.2)(t + 1.2) = 1.64

Calculate the square root of the right side: 1.280624847

Break this problem into two subproblems by setting 
(t + 1.2) equal to 1.280624847 and -1.280624847.

Subproblem 1
t + 1.2 = 1.280624847

Simplifying
t + 1.2 = 1.280624847

Reorder the terms:
1.2 + t = 1.280624847

Solving
1.2 + t = 1.280624847

Solving for variable 't'.

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

Add '-1.2' to each side of the equation.
1.2 + -1.2 + t = 1.280624847 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + t = 1.280624847 + -1.2
t = 1.280624847 + -1.2

Combine like terms: 1.280624847 + -1.2 = 0.080624847
t = 0.080624847

Simplifying
t = 0.080624847

Subproblem 2
t + 1.2 = -1.280624847

Simplifying
t + 1.2 = -1.280624847

Reorder the terms:
1.2 + t = -1.280624847

Solving
1.2 + t = -1.280624847

Solving for variable 't'.

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

Add '-1.2' to each side of the equation.
1.2 + -1.2 + t = -1.280624847 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + t = -1.280624847 + -1.2
t = -1.280624847 + -1.2

Combine like terms: -1.280624847 + -1.2 = -2.480624847
t = -2.480624847

Simplifying
t = -2.480624847

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.080624847, -2.480624847}