81t^2+162t+74=0

Solution for 81t^2+162t+74=0 equation:

Simplifying
81t2 + 162t + 74 = 0

Reorder the terms:
74 + 162t + 81t2 = 0

Solving
74 + 162t + 81t2 = 0

Solving for variable 't'.

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

Divide each side by '81'.
0.9135802469 + 2t + t2 = 0

Move the constant term to the right:

Add '-0.9135802469' to each side of the equation.
0.9135802469 + 2t + -0.9135802469 + t2 = 0 + -0.9135802469

Reorder the terms:
0.9135802469 + -0.9135802469 + 2t + t2 = 0 + -0.9135802469

Combine like terms: 0.9135802469 + -0.9135802469 = 0.0000000000
0.0000000000 + 2t + t2 = 0 + -0.9135802469
2t + t2 = 0 + -0.9135802469

Combine like terms: 0 + -0.9135802469 = -0.9135802469
2t + t2 = -0.9135802469

The t term is 2t.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2t + 1 + t2 = -0.9135802469 + 1

Reorder the terms:
1 + 2t + t2 = -0.9135802469 + 1

Combine like terms: -0.9135802469 + 1 = 0.0864197531
1 + 2t + t2 = 0.0864197531

Factor a perfect square on the left side:
(t + 1)(t + 1) = 0.0864197531

Calculate the square root of the right side: 0.293972368

Break this problem into two subproblems by setting 
(t + 1) equal to 0.293972368 and -0.293972368.

Subproblem 1
t + 1 = 0.293972368

Simplifying
t + 1 = 0.293972368

Reorder the terms:
1 + t = 0.293972368

Solving
1 + t = 0.293972368

Solving for variable 't'.

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

Add '-1' to each side of the equation.
1 + -1 + t = 0.293972368 + -1

Combine like terms: 1 + -1 = 0
0 + t = 0.293972368 + -1
t = 0.293972368 + -1

Combine like terms: 0.293972368 + -1 = -0.706027632
t = -0.706027632

Simplifying
t = -0.706027632

Subproblem 2
t + 1 = -0.293972368

Simplifying
t + 1 = -0.293972368

Reorder the terms:
1 + t = -0.293972368

Solving
1 + t = -0.293972368

Solving for variable 't'.

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

Add '-1' to each side of the equation.
1 + -1 + t = -0.293972368 + -1

Combine like terms: 1 + -1 = 0
0 + t = -0.293972368 + -1
t = -0.293972368 + -1

Combine like terms: -0.293972368 + -1 = -1.293972368
t = -1.293972368

Simplifying
t = -1.293972368

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.706027632, -1.293972368}