6t^2-850t+1=0

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Solution for 6t^2-850t+1=0 equation: 


Simplifying
6t2 + -850t + 1 = 0

Reorder the terms:
1 + -850t + 6t2 = 0

Solving
1 + -850t + 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'.
0.1666666667 + -141.6666667t + t2 = 0

Move the constant term to the right:

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -141.6666667t + -0.1666666667 + t2 = 0 + -0.1666666667

Reorder the terms:
0.1666666667 + -0.1666666667 + -141.6666667t + t2 = 0 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + -141.6666667t + t2 = 0 + -0.1666666667
-141.6666667t + t2 = 0 + -0.1666666667

Combine like terms: 0 + -0.1666666667 = -0.1666666667
-141.6666667t + t2 = -0.1666666667

The t term is -141.6666667t.  Take half its coefficient (-70.83333335).
Square it (5017.361113) and add it to both sides.

Add '5017.361113' to each side of the equation.
-141.6666667t + 5017.361113 + t2 = -0.1666666667 + 5017.361113

Reorder the terms:
5017.361113 + -141.6666667t + t2 = -0.1666666667 + 5017.361113

Combine like terms: -0.1666666667 + 5017.361113 = 5017.1944463333
5017.361113 + -141.6666667t + t2 = 5017.1944463333

Factor a perfect square on the left side:
(t + -70.83333335)(t + -70.83333335) = 5017.1944463333

Calculate the square root of the right side: 70.832156866

Break this problem into two subproblems by setting 
(t + -70.83333335) equal to 70.832156866 and -70.832156866.


Subproblem 1
t + -70.83333335 = 70.832156866

Simplifying
t + -70.83333335 = 70.832156866

Reorder the terms:
-70.83333335 + t = 70.832156866

Solving
-70.83333335 + t = 70.832156866

Solving for variable 't'.

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

Add '70.83333335' to each side of the equation.
-70.83333335 + 70.83333335 + t = 70.832156866 + 70.83333335

Combine like terms: -70.83333335 + 70.83333335 = 0.00000000
0.00000000 + t = 70.832156866 + 70.83333335
t = 70.832156866 + 70.83333335

Combine like terms: 70.832156866 + 70.83333335 = 141.665490216
t = 141.665490216

Simplifying
t = 141.665490216


Subproblem 2
t + -70.83333335 = -70.832156866

Simplifying
t + -70.83333335 = -70.832156866

Reorder the terms:
-70.83333335 + t = -70.832156866

Solving
-70.83333335 + t = -70.832156866

Solving for variable 't'.

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

Add '70.83333335' to each side of the equation.
-70.83333335 + 70.83333335 + t = -70.832156866 + 70.83333335

Combine like terms: -70.83333335 + 70.83333335 = 0.00000000
0.00000000 + t = -70.832156866 + 70.83333335
t = -70.832156866 + 70.83333335

Combine like terms: -70.832156866 + 70.83333335 = 0.001176484
t = 0.001176484

Simplifying
t = 0.001176484


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {141.665490216, 0.001176484}

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