6t^2-t-8=0

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Solution for 6t^2-t-8=0 equation: 


Simplifying
6t2 + -1t + -8 = 0

Reorder the terms:
-8 + -1t + 6t2 = 0

Solving
-8 + -1t + 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'.
-1.333333333 + -0.1666666667t + t2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + -0.1666666667t + 1.333333333 + t2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + -0.1666666667t + t2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + -0.1666666667t + t2 = 0 + 1.333333333
-0.1666666667t + t2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
-0.1666666667t + t2 = 1.333333333

The t term is -0.1666666667t.  Take half its coefficient (-0.08333333335).
Square it (0.006944444447) and add it to both sides.

Add '0.006944444447' to each side of the equation.
-0.1666666667t + 0.006944444447 + t2 = 1.333333333 + 0.006944444447

Reorder the terms:
0.006944444447 + -0.1666666667t + t2 = 1.333333333 + 0.006944444447

Combine like terms: 1.333333333 + 0.006944444447 = 1.340277777447
0.006944444447 + -0.1666666667t + t2 = 1.340277777447

Factor a perfect square on the left side:
(t + -0.08333333335)(t + -0.08333333335) = 1.340277777447

Calculate the square root of the right side: 1.157703666

Break this problem into two subproblems by setting 
(t + -0.08333333335) equal to 1.157703666 and -1.157703666.


Subproblem 1
t + -0.08333333335 = 1.157703666

Simplifying
t + -0.08333333335 = 1.157703666

Reorder the terms:
-0.08333333335 + t = 1.157703666

Solving
-0.08333333335 + t = 1.157703666

Solving for variable 't'.

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

Add '0.08333333335' to each side of the equation.
-0.08333333335 + 0.08333333335 + t = 1.157703666 + 0.08333333335

Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000
0.00000000000 + t = 1.157703666 + 0.08333333335
t = 1.157703666 + 0.08333333335

Combine like terms: 1.157703666 + 0.08333333335 = 1.24103699935
t = 1.24103699935

Simplifying
t = 1.24103699935


Subproblem 2
t + -0.08333333335 = -1.157703666

Simplifying
t + -0.08333333335 = -1.157703666

Reorder the terms:
-0.08333333335 + t = -1.157703666

Solving
-0.08333333335 + t = -1.157703666

Solving for variable 't'.

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

Add '0.08333333335' to each side of the equation.
-0.08333333335 + 0.08333333335 + t = -1.157703666 + 0.08333333335

Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000
0.00000000000 + t = -1.157703666 + 0.08333333335
t = -1.157703666 + 0.08333333335

Combine like terms: -1.157703666 + 0.08333333335 = -1.07437033265
t = -1.07437033265

Simplifying
t = -1.07437033265


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.24103699935, -1.07437033265}

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