7=1+15t-5t^2

Solution for 7=1+15t-5t^2 equation:

Simplifying
7 = 1 + 15t + -5t2

Solving
7 = 1 + 15t + -5t2

Solving for variable 't'.

Combine like terms: 7 + -1 = 6
6 + -15t + 5t2 = 1 + 15t + -5t2 + -1 + -15t + 5t2

Reorder the terms:
6 + -15t + 5t2 = 1 + -1 + 15t + -15t + -5t2 + 5t2

Combine like terms: 1 + -1 = 0
6 + -15t + 5t2 = 0 + 15t + -15t + -5t2 + 5t2
6 + -15t + 5t2 = 15t + -15t + -5t2 + 5t2

Combine like terms: 15t + -15t = 0
6 + -15t + 5t2 = 0 + -5t2 + 5t2
6 + -15t + 5t2 = -5t2 + 5t2

Combine like terms: -5t2 + 5t2 = 0
6 + -15t + 5t2 = 0

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

Divide each side by '5'.
1.2 + -3t + t2 = 0

Move the constant term to the right:

Add '-1.2' to each side of the equation.
1.2 + -3t + -1.2 + t2 = 0 + -1.2

Reorder the terms:
1.2 + -1.2 + -3t + t2 = 0 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + -3t + t2 = 0 + -1.2
-3t + t2 = 0 + -1.2

Combine like terms: 0 + -1.2 = -1.2
-3t + t2 = -1.2

The t term is -3t.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3t + 2.25 + t2 = -1.2 + 2.25

Reorder the terms:
2.25 + -3t + t2 = -1.2 + 2.25

Combine like terms: -1.2 + 2.25 = 1.05
2.25 + -3t + t2 = 1.05

Factor a perfect square on the left side:
(t + -1.5)(t + -1.5) = 1.05

Calculate the square root of the right side: 1.024695077

Break this problem into two subproblems by setting 
(t + -1.5) equal to 1.024695077 and -1.024695077.

Subproblem 1
t + -1.5 = 1.024695077

Simplifying
t + -1.5 = 1.024695077

Reorder the terms:
-1.5 + t = 1.024695077

Solving
-1.5 + t = 1.024695077

Solving for variable 't'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + t = 1.024695077 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = 1.024695077 + 1.5
t = 1.024695077 + 1.5

Combine like terms: 1.024695077 + 1.5 = 2.524695077
t = 2.524695077

Simplifying
t = 2.524695077

Subproblem 2
t + -1.5 = -1.024695077

Simplifying
t + -1.5 = -1.024695077

Reorder the terms:
-1.5 + t = -1.024695077

Solving
-1.5 + t = -1.024695077

Solving for variable 't'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + t = -1.024695077 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = -1.024695077 + 1.5
t = -1.024695077 + 1.5

Combine like terms: -1.024695077 + 1.5 = 0.475304923
t = 0.475304923

Simplifying
t = 0.475304923

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.524695077, 0.475304923}