-.15t^2+5t-17=0

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Solution for -.15t^2+5t-17=0 equation: 


Simplifying
-0.15t2 + 5t + -17 = 0

Reorder the terms:
-17 + 5t + -0.15t2 = 0

Solving
-17 + 5t + -0.15t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
-0.15 the coefficient of the squared term: 

Divide each side by '-0.15'.
113.3333333 + -33.33333333t + t2 = 0

Move the constant term to the right:

Add '-113.3333333' to each side of the equation.
113.3333333 + -33.33333333t + -113.3333333 + t2 = 0 + -113.3333333

Reorder the terms:
113.3333333 + -113.3333333 + -33.33333333t + t2 = 0 + -113.3333333

Combine like terms: 113.3333333 + -113.3333333 = 0.0000000
0.0000000 + -33.33333333t + t2 = 0 + -113.3333333
-33.33333333t + t2 = 0 + -113.3333333

Combine like terms: 0 + -113.3333333 = -113.3333333
-33.33333333t + t2 = -113.3333333

The t term is -33.33333333t.  Take half its coefficient (-16.66666667).
Square it (277.7777779) and add it to both sides.

Add '277.7777779' to each side of the equation.
-33.33333333t + 277.7777779 + t2 = -113.3333333 + 277.7777779

Reorder the terms:
277.7777779 + -33.33333333t + t2 = -113.3333333 + 277.7777779

Combine like terms: -113.3333333 + 277.7777779 = 164.4444446
277.7777779 + -33.33333333t + t2 = 164.4444446

Factor a perfect square on the left side:
(t + -16.66666667)(t + -16.66666667) = 164.4444446

Calculate the square root of the right side: 12.823589381

Break this problem into two subproblems by setting 
(t + -16.66666667) equal to 12.823589381 and -12.823589381.


Subproblem 1
t + -16.66666667 = 12.823589381

Simplifying
t + -16.66666667 = 12.823589381

Reorder the terms:
-16.66666667 + t = 12.823589381

Solving
-16.66666667 + t = 12.823589381

Solving for variable 't'.

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

Add '16.66666667' to each side of the equation.
-16.66666667 + 16.66666667 + t = 12.823589381 + 16.66666667

Combine like terms: -16.66666667 + 16.66666667 = 0.00000000
0.00000000 + t = 12.823589381 + 16.66666667
t = 12.823589381 + 16.66666667

Combine like terms: 12.823589381 + 16.66666667 = 29.490256051
t = 29.490256051

Simplifying
t = 29.490256051


Subproblem 2
t + -16.66666667 = -12.823589381

Simplifying
t + -16.66666667 = -12.823589381

Reorder the terms:
-16.66666667 + t = -12.823589381

Solving
-16.66666667 + t = -12.823589381

Solving for variable 't'.

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

Add '16.66666667' to each side of the equation.
-16.66666667 + 16.66666667 + t = -12.823589381 + 16.66666667

Combine like terms: -16.66666667 + 16.66666667 = 0.00000000
0.00000000 + t = -12.823589381 + 16.66666667
t = -12.823589381 + 16.66666667

Combine like terms: -12.823589381 + 16.66666667 = 3.843077289
t = 3.843077289

Simplifying
t = 3.843077289


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {29.490256051, 3.843077289}

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