-5t^2+15t+0.5=10

Solution for -5t^2+15t+0.5=10 equation:

Simplifying
-5t2 + 15t + 0.5 = 10

Reorder the terms:
0.5 + 15t + -5t2 = 10

Solving
0.5 + 15t + -5t2 = 10

Solving for variable 't'.

Reorder the terms:
0.5 + -10 + 15t + -5t2 = 10 + -10

Combine like terms: 0.5 + -10 = -9.5
-9.5 + 15t + -5t2 = 10 + -10

Combine like terms: 10 + -10 = 0
-9.5 + 15t + -5t2 = 0

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

Divide each side by '-5'.
1.9 + -3t + t2 = 0

Move the constant term to the right:

Add '-1.9' to each side of the equation.
1.9 + -3t + -1.9 + t2 = 0 + -1.9

Reorder the terms:
1.9 + -1.9 + -3t + t2 = 0 + -1.9

Combine like terms: 1.9 + -1.9 = 0.0
0.0 + -3t + t2 = 0 + -1.9
-3t + t2 = 0 + -1.9

Combine like terms: 0 + -1.9 = -1.9
-3t + t2 = -1.9

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 = -1.9 + 2.25

Reorder the terms:
2.25 + -3t + t2 = -1.9 + 2.25

Combine like terms: -1.9 + 2.25 = 0.35
2.25 + -3t + t2 = 0.35

Factor a perfect square on the left side:
(t + -1.5)(t + -1.5) = 0.35

Calculate the square root of the right side: 0.591607978

Break this problem into two subproblems by setting 
(t + -1.5) equal to 0.591607978 and -0.591607978.

Subproblem 1
t + -1.5 = 0.591607978

Simplifying
t + -1.5 = 0.591607978

Reorder the terms:
-1.5 + t = 0.591607978

Solving
-1.5 + t = 0.591607978

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 = 0.591607978 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = 0.591607978 + 1.5
t = 0.591607978 + 1.5

Combine like terms: 0.591607978 + 1.5 = 2.091607978
t = 2.091607978

Simplifying
t = 2.091607978

Subproblem 2
t + -1.5 = -0.591607978

Simplifying
t + -1.5 = -0.591607978

Reorder the terms:
-1.5 + t = -0.591607978

Solving
-1.5 + t = -0.591607978

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 = -0.591607978 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = -0.591607978 + 1.5
t = -0.591607978 + 1.5

Combine like terms: -0.591607978 + 1.5 = 0.908392022
t = 0.908392022

Simplifying
t = 0.908392022

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.091607978, 0.908392022}