0.5=-5t^2+15t

Solution for 0.5=-5t^2+15t equation:

Simplifying
0.5 = -5t2 + 15t

Reorder the terms:
0.5 = 15t + -5t2

Solving
0.5 = 15t + -5t2

Solving for variable 't'.

Reorder the terms:
0.5 + -15t + 5t2 = 15t + -15t + -5t2 + 5t2

Combine like terms: 15t + -15t = 0
0.5 + -15t + 5t2 = 0 + -5t2 + 5t2
0.5 + -15t + 5t2 = -5t2 + 5t2

Combine like terms: -5t2 + 5t2 = 0
0.5 + -15t + 5t2 = 0

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

Divide each side by '5'.
0.1 + -3t + t2 = 0

Move the constant term to the right:

Add '-0.1' to each side of the equation.
0.1 + -3t + -0.1 + t2 = 0 + -0.1

Reorder the terms:
0.1 + -0.1 + -3t + t2 = 0 + -0.1

Combine like terms: 0.1 + -0.1 = 0.0
0.0 + -3t + t2 = 0 + -0.1
-3t + t2 = 0 + -0.1

Combine like terms: 0 + -0.1 = -0.1
-3t + t2 = -0.1

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 = -0.1 + 2.25

Reorder the terms:
2.25 + -3t + t2 = -0.1 + 2.25

Combine like terms: -0.1 + 2.25 = 2.15
2.25 + -3t + t2 = 2.15

Factor a perfect square on the left side:
(t + -1.5)(t + -1.5) = 2.15

Calculate the square root of the right side: 1.46628783

Break this problem into two subproblems by setting 
(t + -1.5) equal to 1.46628783 and -1.46628783.

Subproblem 1
t + -1.5 = 1.46628783

Simplifying
t + -1.5 = 1.46628783

Reorder the terms:
-1.5 + t = 1.46628783

Solving
-1.5 + t = 1.46628783

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 = 1.46628783 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = 1.46628783 + 1.5
t = 1.46628783 + 1.5

Combine like terms: 1.46628783 + 1.5 = 2.96628783
t = 2.96628783

Simplifying
t = 2.96628783

Subproblem 2
t + -1.5 = -1.46628783

Simplifying
t + -1.5 = -1.46628783

Reorder the terms:
-1.5 + t = -1.46628783

Solving
-1.5 + t = -1.46628783

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 = -1.46628783 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = -1.46628783 + 1.5
t = -1.46628783 + 1.5

Combine like terms: -1.46628783 + 1.5 = 0.03371217
t = 0.03371217

Simplifying
t = 0.03371217

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.96628783, 0.03371217}