76=-13t+5t^2

Solution for 76=-13t+5t^2 equation:

Simplifying
76 = -13t + 5t2

Solving
76 = -13t + 5t2

Solving for variable 't'.

Reorder the terms:
76 + 13t + -5t2 = -13t + 13t + 5t2 + -5t2

Combine like terms: -13t + 13t = 0
76 + 13t + -5t2 = 0 + 5t2 + -5t2
76 + 13t + -5t2 = 5t2 + -5t2

Combine like terms: 5t2 + -5t2 = 0
76 + 13t + -5t2 = 0

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

Divide each side by '-5'.
-15.2 + -2.6t + t2 = 0

Move the constant term to the right:

Add '15.2' to each side of the equation.
-15.2 + -2.6t + 15.2 + t2 = 0 + 15.2

Reorder the terms:
-15.2 + 15.2 + -2.6t + t2 = 0 + 15.2

Combine like terms: -15.2 + 15.2 = 0.0
0.0 + -2.6t + t2 = 0 + 15.2
-2.6t + t2 = 0 + 15.2

Combine like terms: 0 + 15.2 = 15.2
-2.6t + t2 = 15.2

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 = 15.2 + 1.69

Reorder the terms:
1.69 + -2.6t + t2 = 15.2 + 1.69

Combine like terms: 15.2 + 1.69 = 16.89
1.69 + -2.6t + t2 = 16.89

Factor a perfect square on the left side:
(t + -1.3)(t + -1.3) = 16.89

Calculate the square root of the right side: 4.109744518

Break this problem into two subproblems by setting 
(t + -1.3) equal to 4.109744518 and -4.109744518.

Subproblem 1
t + -1.3 = 4.109744518

Simplifying
t + -1.3 = 4.109744518

Reorder the terms:
-1.3 + t = 4.109744518

Solving
-1.3 + t = 4.109744518

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 = 4.109744518 + 1.3

Combine like terms: -1.3 + 1.3 = 0.0
0.0 + t = 4.109744518 + 1.3
t = 4.109744518 + 1.3

Combine like terms: 4.109744518 + 1.3 = 5.409744518
t = 5.409744518

Simplifying
t = 5.409744518

Subproblem 2
t + -1.3 = -4.109744518

Simplifying
t + -1.3 = -4.109744518

Reorder the terms:
-1.3 + t = -4.109744518

Solving
-1.3 + t = -4.109744518

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 = -4.109744518 + 1.3

Combine like terms: -1.3 + 1.3 = 0.0
0.0 + t = -4.109744518 + 1.3
t = -4.109744518 + 1.3

Combine like terms: -4.109744518 + 1.3 = -2.809744518
t = -2.809744518

Simplifying
t = -2.809744518

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {5.409744518, -2.809744518}