3+15t-5t^2=11

Solution for 3+15t-5t^2=11 equation:

Simplifying
3 + 15t + -5t2 = 11

Solving
3 + 15t + -5t2 = 11

Solving for variable 't'.

Reorder the terms:
3 + -11 + 15t + -5t2 = 11 + -11

Combine like terms: 3 + -11 = -8
-8 + 15t + -5t2 = 11 + -11

Combine like terms: 11 + -11 = 0
-8 + 15t + -5t2 = 0

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

Divide each side by '-5'.
1.6 + -3t + t2 = 0

Move the constant term to the right:

Add '-1.6' to each side of the equation.
1.6 + -3t + -1.6 + t2 = 0 + -1.6

Reorder the terms:
1.6 + -1.6 + -3t + t2 = 0 + -1.6

Combine like terms: 1.6 + -1.6 = 0.0
0.0 + -3t + t2 = 0 + -1.6
-3t + t2 = 0 + -1.6

Combine like terms: 0 + -1.6 = -1.6
-3t + t2 = -1.6

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 = -1.6 + 2.25

Reorder the terms:
2.25 + -3t + t2 = -1.6 + 2.25

Combine like terms: -1.6 + 2.25 = 0.65
2.25 + -3t + t2 = 0.65

Factor a perfect square on the left side:
(t + -1.5)(t + -1.5) = 0.65

Calculate the square root of the right side: 0.806225775

Break this problem into two subproblems by setting 
(t + -1.5) equal to 0.806225775 and -0.806225775.

Subproblem 1
t + -1.5 = 0.806225775

Simplifying
t + -1.5 = 0.806225775

Reorder the terms:
-1.5 + t = 0.806225775

Solving
-1.5 + t = 0.806225775

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 = 0.806225775 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = 0.806225775 + 1.5
t = 0.806225775 + 1.5

Combine like terms: 0.806225775 + 1.5 = 2.306225775
t = 2.306225775

Simplifying
t = 2.306225775

Subproblem 2
t + -1.5 = -0.806225775

Simplifying
t + -1.5 = -0.806225775

Reorder the terms:
-1.5 + t = -0.806225775

Solving
-1.5 + t = -0.806225775

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 = -0.806225775 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = -0.806225775 + 1.5
t = -0.806225775 + 1.5

Combine like terms: -0.806225775 + 1.5 = 0.693774225
t = 0.693774225

Simplifying
t = 0.693774225

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.306225775, 0.693774225}