0=-5t^2+6t+1.5

Solution for 0=-5t^2+6t+1.5 equation:

Simplifying
0 = -5t2 + 6t + 1.5

Reorder the terms:
0 = 1.5 + 6t + -5t2

Solving
0 = 1.5 + 6t + -5t2

Solving for variable 't'.

Combine like terms: 0 + -1.5 = -1.5
-1.5 + -6t + 5t2 = 1.5 + 6t + -5t2 + -1.5 + -6t + 5t2

Reorder the terms:
-1.5 + -6t + 5t2 = 1.5 + -1.5 + 6t + -6t + -5t2 + 5t2

Combine like terms: 1.5 + -1.5 = 0.0
-1.5 + -6t + 5t2 = 0.0 + 6t + -6t + -5t2 + 5t2
-1.5 + -6t + 5t2 = 6t + -6t + -5t2 + 5t2

Combine like terms: 6t + -6t = 0
-1.5 + -6t + 5t2 = 0 + -5t2 + 5t2
-1.5 + -6t + 5t2 = -5t2 + 5t2

Combine like terms: -5t2 + 5t2 = 0
-1.5 + -6t + 5t2 = 0

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

Divide each side by '5'.
-0.3 + -1.2t + t2 = 0

Move the constant term to the right:

Add '0.3' to each side of the equation.
-0.3 + -1.2t + 0.3 + t2 = 0 + 0.3

Reorder the terms:
-0.3 + 0.3 + -1.2t + t2 = 0 + 0.3

Combine like terms: -0.3 + 0.3 = 0.0
0.0 + -1.2t + t2 = 0 + 0.3
-1.2t + t2 = 0 + 0.3

Combine like terms: 0 + 0.3 = 0.3
-1.2t + t2 = 0.3

The t term is -1.2t.  Take half its coefficient (-0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
-1.2t + 0.36 + t2 = 0.3 + 0.36

Reorder the terms:
0.36 + -1.2t + t2 = 0.3 + 0.36

Combine like terms: 0.3 + 0.36 = 0.66
0.36 + -1.2t + t2 = 0.66

Factor a perfect square on the left side:
(t + -0.6)(t + -0.6) = 0.66

Calculate the square root of the right side: 0.81240384

Break this problem into two subproblems by setting 
(t + -0.6) equal to 0.81240384 and -0.81240384.

Subproblem 1
t + -0.6 = 0.81240384

Simplifying
t + -0.6 = 0.81240384

Reorder the terms:
-0.6 + t = 0.81240384

Solving
-0.6 + t = 0.81240384

Solving for variable 't'.

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

Add '0.6' to each side of the equation.
-0.6 + 0.6 + t = 0.81240384 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + t = 0.81240384 + 0.6
t = 0.81240384 + 0.6

Combine like terms: 0.81240384 + 0.6 = 1.41240384
t = 1.41240384

Simplifying
t = 1.41240384

Subproblem 2
t + -0.6 = -0.81240384

Simplifying
t + -0.6 = -0.81240384

Reorder the terms:
-0.6 + t = -0.81240384

Solving
-0.6 + t = -0.81240384

Solving for variable 't'.

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

Add '0.6' to each side of the equation.
-0.6 + 0.6 + t = -0.81240384 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + t = -0.81240384 + 0.6
t = -0.81240384 + 0.6

Combine like terms: -0.81240384 + 0.6 = -0.21240384
t = -0.21240384

Simplifying
t = -0.21240384

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.41240384, -0.21240384}