0=79-6t-5t^2

Solution for 0=79-6t-5t^2 equation:

Simplifying
0 = 79 + -6t + -5t2

Solving
0 = 79 + -6t + -5t2

Solving for variable 't'.

Combine like terms: 0 + -79 = -79
-79 + 6t + 5t2 = 79 + -6t + -5t2 + -79 + 6t + 5t2

Reorder the terms:
-79 + 6t + 5t2 = 79 + -79 + -6t + 6t + -5t2 + 5t2

Combine like terms: 79 + -79 = 0
-79 + 6t + 5t2 = 0 + -6t + 6t + -5t2 + 5t2
-79 + 6t + 5t2 = -6t + 6t + -5t2 + 5t2

Combine like terms: -6t + 6t = 0
-79 + 6t + 5t2 = 0 + -5t2 + 5t2
-79 + 6t + 5t2 = -5t2 + 5t2

Combine like terms: -5t2 + 5t2 = 0
-79 + 6t + 5t2 = 0

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

Divide each side by '5'.
-15.8 + 1.2t + t2 = 0

Move the constant term to the right:

Add '15.8' to each side of the equation.
-15.8 + 1.2t + 15.8 + t2 = 0 + 15.8

Reorder the terms:
-15.8 + 15.8 + 1.2t + t2 = 0 + 15.8

Combine like terms: -15.8 + 15.8 = 0.0
0.0 + 1.2t + t2 = 0 + 15.8
1.2t + t2 = 0 + 15.8

Combine like terms: 0 + 15.8 = 15.8
1.2t + t2 = 15.8

The t term is 1.2t.  Take half its coefficient (0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
1.2t + 0.36 + t2 = 15.8 + 0.36

Reorder the terms:
0.36 + 1.2t + t2 = 15.8 + 0.36

Combine like terms: 15.8 + 0.36 = 16.16
0.36 + 1.2t + t2 = 16.16

Factor a perfect square on the left side:
(t + 0.6)(t + 0.6) = 16.16

Calculate the square root of the right side: 4.019950248

Break this problem into two subproblems by setting 
(t + 0.6) equal to 4.019950248 and -4.019950248.

Subproblem 1
t + 0.6 = 4.019950248

Simplifying
t + 0.6 = 4.019950248

Reorder the terms:
0.6 + t = 4.019950248

Solving
0.6 + t = 4.019950248

Solving for variable 't'.

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

Add '-0.6' to each side of the equation.
0.6 + -0.6 + t = 4.019950248 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + t = 4.019950248 + -0.6
t = 4.019950248 + -0.6

Combine like terms: 4.019950248 + -0.6 = 3.419950248
t = 3.419950248

Simplifying
t = 3.419950248

Subproblem 2
t + 0.6 = -4.019950248

Simplifying
t + 0.6 = -4.019950248

Reorder the terms:
0.6 + t = -4.019950248

Solving
0.6 + t = -4.019950248

Solving for variable 't'.

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

Add '-0.6' to each side of the equation.
0.6 + -0.6 + t = -4.019950248 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + t = -4.019950248 + -0.6
t = -4.019950248 + -0.6

Combine like terms: -4.019950248 + -0.6 = -4.619950248
t = -4.619950248

Simplifying
t = -4.619950248

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.419950248, -4.619950248}