(t)=7-12t+5t^2

Solution for (t)=7-12t+5t^2 equation:

Simplifying
(t) = 7 + -12t + 5t2
t = 7 + -12t + 5t2

Solving
t = 7 + -12t + 5t2

Solving for variable 't'.

Reorder the terms:
-7 + t + 12t + -5t2 = 7 + -12t + 5t2 + -7 + 12t + -5t2

Combine like terms: t + 12t = 13t
-7 + 13t + -5t2 = 7 + -12t + 5t2 + -7 + 12t + -5t2

Reorder the terms:
-7 + 13t + -5t2 = 7 + -7 + -12t + 12t + 5t2 + -5t2

Combine like terms: 7 + -7 = 0
-7 + 13t + -5t2 = 0 + -12t + 12t + 5t2 + -5t2
-7 + 13t + -5t2 = -12t + 12t + 5t2 + -5t2

Combine like terms: -12t + 12t = 0
-7 + 13t + -5t2 = 0 + 5t2 + -5t2
-7 + 13t + -5t2 = 5t2 + -5t2

Combine like terms: 5t2 + -5t2 = 0
-7 + 13t + -5t2 = 0

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

Divide each side by '-5'.
1.4 + -2.6t + t2 = 0

Move the constant term to the right:

Add '-1.4' to each side of the equation.
1.4 + -2.6t + -1.4 + t2 = 0 + -1.4

Reorder the terms:
1.4 + -1.4 + -2.6t + t2 = 0 + -1.4

Combine like terms: 1.4 + -1.4 = 0.0
0.0 + -2.6t + t2 = 0 + -1.4
-2.6t + t2 = 0 + -1.4

Combine like terms: 0 + -1.4 = -1.4
-2.6t + t2 = -1.4

The t term is -2.6t.  Take half its coefficient (-1.3).
Square it (1.69) and add it to both sides.

Add '1.69' to each side of the equation.
-2.6t + 1.69 + t2 = -1.4 + 1.69

Reorder the terms:
1.69 + -2.6t + t2 = -1.4 + 1.69

Combine like terms: -1.4 + 1.69 = 0.29
1.69 + -2.6t + t2 = 0.29

Factor a perfect square on the left side:
(t + -1.3)(t + -1.3) = 0.29

Calculate the square root of the right side: 0.538516481

Break this problem into two subproblems by setting 
(t + -1.3) equal to 0.538516481 and -0.538516481.

Subproblem 1
t + -1.3 = 0.538516481

Simplifying
t + -1.3 = 0.538516481

Reorder the terms:
-1.3 + t = 0.538516481

Solving
-1.3 + t = 0.538516481

Solving for variable 't'.

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

Add '1.3' to each side of the equation.
-1.3 + 1.3 + t = 0.538516481 + 1.3

Combine like terms: -1.3 + 1.3 = 0.0
0.0 + t = 0.538516481 + 1.3
t = 0.538516481 + 1.3

Combine like terms: 0.538516481 + 1.3 = 1.838516481
t = 1.838516481

Simplifying
t = 1.838516481

Subproblem 2
t + -1.3 = -0.538516481

Simplifying
t + -1.3 = -0.538516481

Reorder the terms:
-1.3 + t = -0.538516481

Solving
-1.3 + t = -0.538516481

Solving for variable 't'.

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

Add '1.3' to each side of the equation.
-1.3 + 1.3 + t = -0.538516481 + 1.3

Combine like terms: -1.3 + 1.3 = 0.0
0.0 + t = -0.538516481 + 1.3
t = -0.538516481 + 1.3

Combine like terms: -0.538516481 + 1.3 = 0.761483519
t = 0.761483519

Simplifying
t = 0.761483519

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.838516481, 0.761483519}