6t^2+13t-7=0

Solution for 6t^2+13t-7=0 equation:

Simplifying
6t2 + 13t + -7 = 0

Reorder the terms:
-7 + 13t + 6t2 = 0

Solving
-7 + 13t + 6t2 = 0

Solving for variable 't'.

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

Divide each side by '6'.
-1.166666667 + 2.166666667t + t2 = 0

Move the constant term to the right:

Add '1.166666667' to each side of the equation.
-1.166666667 + 2.166666667t + 1.166666667 + t2 = 0 + 1.166666667

Reorder the terms:
-1.166666667 + 1.166666667 + 2.166666667t + t2 = 0 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + 2.166666667t + t2 = 0 + 1.166666667
2.166666667t + t2 = 0 + 1.166666667

Combine like terms: 0 + 1.166666667 = 1.166666667
2.166666667t + t2 = 1.166666667

The t term is 2.166666667t.  Take half its coefficient (1.083333334).
Square it (1.173611113) and add it to both sides.

Add '1.173611113' to each side of the equation.
2.166666667t + 1.173611113 + t2 = 1.166666667 + 1.173611113

Reorder the terms:
1.173611113 + 2.166666667t + t2 = 1.166666667 + 1.173611113

Combine like terms: 1.166666667 + 1.173611113 = 2.34027778
1.173611113 + 2.166666667t + t2 = 2.34027778

Factor a perfect square on the left side:
(t + 1.083333334)(t + 1.083333334) = 2.34027778

Calculate the square root of the right side: 1.529796647

Break this problem into two subproblems by setting 
(t + 1.083333334) equal to 1.529796647 and -1.529796647.

Subproblem 1
t + 1.083333334 = 1.529796647

Simplifying
t + 1.083333334 = 1.529796647

Reorder the terms:
1.083333334 + t = 1.529796647

Solving
1.083333334 + t = 1.529796647

Solving for variable 't'.

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

Add '-1.083333334' to each side of the equation.
1.083333334 + -1.083333334 + t = 1.529796647 + -1.083333334

Combine like terms: 1.083333334 + -1.083333334 = 0.000000000
0.000000000 + t = 1.529796647 + -1.083333334
t = 1.529796647 + -1.083333334

Combine like terms: 1.529796647 + -1.083333334 = 0.446463313
t = 0.446463313

Simplifying
t = 0.446463313

Subproblem 2
t + 1.083333334 = -1.529796647

Simplifying
t + 1.083333334 = -1.529796647

Reorder the terms:
1.083333334 + t = -1.529796647

Solving
1.083333334 + t = -1.529796647

Solving for variable 't'.

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

Add '-1.083333334' to each side of the equation.
1.083333334 + -1.083333334 + t = -1.529796647 + -1.083333334

Combine like terms: 1.083333334 + -1.083333334 = 0.000000000
0.000000000 + t = -1.529796647 + -1.083333334
t = -1.529796647 + -1.083333334

Combine like terms: -1.529796647 + -1.083333334 = -2.613129981
t = -2.613129981

Simplifying
t = -2.613129981

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.446463313, -2.613129981}