(-10)t^2-66.6t+6=0

Solution for (-10)t^2-66.6t+6=0 equation:

Simplifying
(-10) * t2 + -66.6t + 6 = 0

Reorder the terms:
6 + -66.6t + -10t2 = 0

Solving
6 + -66.6t + -10t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
-10 the coefficient of the squared term: 

Divide each side by '-10'.
-0.6 + 6.66t + t2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + 6.66t + 0.6 + t2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + 6.66t + t2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + 6.66t + t2 = 0 + 0.6
6.66t + t2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
6.66t + t2 = 0.6

The t term is 6.66t.  Take half its coefficient (3.33).
Square it (11.0889) and add it to both sides.

Add '11.0889' to each side of the equation.
6.66t + 11.0889 + t2 = 0.6 + 11.0889

Reorder the terms:
11.0889 + 6.66t + t2 = 0.6 + 11.0889

Combine like terms: 0.6 + 11.0889 = 11.6889
11.0889 + 6.66t + t2 = 11.6889

Factor a perfect square on the left side:
(t + 3.33)(t + 3.33) = 11.6889

Calculate the square root of the right side: 3.418903333

Break this problem into two subproblems by setting 
(t + 3.33) equal to 3.418903333 and -3.418903333.

Subproblem 1
t + 3.33 = 3.418903333

Simplifying
t + 3.33 = 3.418903333

Reorder the terms:
3.33 + t = 3.418903333

Solving
3.33 + t = 3.418903333

Solving for variable 't'.

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

Add '-3.33' to each side of the equation.
3.33 + -3.33 + t = 3.418903333 + -3.33

Combine like terms: 3.33 + -3.33 = 0.00
0.00 + t = 3.418903333 + -3.33
t = 3.418903333 + -3.33

Combine like terms: 3.418903333 + -3.33 = 0.088903333
t = 0.088903333

Simplifying
t = 0.088903333

Subproblem 2
t + 3.33 = -3.418903333

Simplifying
t + 3.33 = -3.418903333

Reorder the terms:
3.33 + t = -3.418903333

Solving
3.33 + t = -3.418903333

Solving for variable 't'.

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

Add '-3.33' to each side of the equation.
3.33 + -3.33 + t = -3.418903333 + -3.33

Combine like terms: 3.33 + -3.33 = 0.00
0.00 + t = -3.418903333 + -3.33
t = -3.418903333 + -3.33

Combine like terms: -3.418903333 + -3.33 = -6.748903333
t = -6.748903333

Simplifying
t = -6.748903333

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.088903333, -6.748903333}