3t^2-16t+15=0

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Solution for 3t^2-16t+15=0 equation: 


Simplifying
3t2 + -16t + 15 = 0

Reorder the terms:
15 + -16t + 3t2 = 0

Solving
15 + -16t + 3t2 = 0

Solving for variable 't'.

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

Divide each side by '3'.
5 + -5.333333333t + t2 = 0

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -5.333333333t + -5 + t2 = 0 + -5

Reorder the terms:
5 + -5 + -5.333333333t + t2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -5.333333333t + t2 = 0 + -5
-5.333333333t + t2 = 0 + -5

Combine like terms: 0 + -5 = -5
-5.333333333t + t2 = -5

The t term is -5.333333333t.  Take half its coefficient (-2.666666667).
Square it (7.111111113) and add it to both sides.

Add '7.111111113' to each side of the equation.
-5.333333333t + 7.111111113 + t2 = -5 + 7.111111113

Reorder the terms:
7.111111113 + -5.333333333t + t2 = -5 + 7.111111113

Combine like terms: -5 + 7.111111113 = 2.111111113
7.111111113 + -5.333333333t + t2 = 2.111111113

Factor a perfect square on the left side:
(t + -2.666666667)(t + -2.666666667) = 2.111111113

Calculate the square root of the right side: 1.452966315

Break this problem into two subproblems by setting 
(t + -2.666666667) equal to 1.452966315 and -1.452966315.


Subproblem 1
t + -2.666666667 = 1.452966315

Simplifying
t + -2.666666667 = 1.452966315

Reorder the terms:
-2.666666667 + t = 1.452966315

Solving
-2.666666667 + t = 1.452966315

Solving for variable 't'.

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

Add '2.666666667' to each side of the equation.
-2.666666667 + 2.666666667 + t = 1.452966315 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + t = 1.452966315 + 2.666666667
t = 1.452966315 + 2.666666667

Combine like terms: 1.452966315 + 2.666666667 = 4.119632982
t = 4.119632982

Simplifying
t = 4.119632982


Subproblem 2
t + -2.666666667 = -1.452966315

Simplifying
t + -2.666666667 = -1.452966315

Reorder the terms:
-2.666666667 + t = -1.452966315

Solving
-2.666666667 + t = -1.452966315

Solving for variable 't'.

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

Add '2.666666667' to each side of the equation.
-2.666666667 + 2.666666667 + t = -1.452966315 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + t = -1.452966315 + 2.666666667
t = -1.452966315 + 2.666666667

Combine like terms: -1.452966315 + 2.666666667 = 1.213700352
t = 1.213700352

Simplifying
t = 1.213700352


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.119632982, 1.213700352}

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