0.5t^2+2t-150=0

Solution for 0.5t^2+2t-150=0 equation:

Simplifying
0.5t2 + 2t + -150 = 0

Reorder the terms:
-150 + 2t + 0.5t2 = 0

Solving
-150 + 2t + 0.5t2 = 0

Solving for variable 't'.

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

Divide each side by '0.5'.
-300 + 4t + t2 = 0

Move the constant term to the right:

Add '300' to each side of the equation.
-300 + 4t + 300 + t2 = 0 + 300

Reorder the terms:
-300 + 300 + 4t + t2 = 0 + 300

Combine like terms: -300 + 300 = 0
0 + 4t + t2 = 0 + 300
4t + t2 = 0 + 300

Combine like terms: 0 + 300 = 300
4t + t2 = 300

The t term is 4t.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4t + 4 + t2 = 300 + 4

Reorder the terms:
4 + 4t + t2 = 300 + 4

Combine like terms: 300 + 4 = 304
4 + 4t + t2 = 304

Factor a perfect square on the left side:
(t + 2)(t + 2) = 304

Calculate the square root of the right side: 17.435595774

Break this problem into two subproblems by setting 
(t + 2) equal to 17.435595774 and -17.435595774.

Subproblem 1
t + 2 = 17.435595774

Simplifying
t + 2 = 17.435595774

Reorder the terms:
2 + t = 17.435595774

Solving
2 + t = 17.435595774

Solving for variable 't'.

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

Add '-2' to each side of the equation.
2 + -2 + t = 17.435595774 + -2

Combine like terms: 2 + -2 = 0
0 + t = 17.435595774 + -2
t = 17.435595774 + -2

Combine like terms: 17.435595774 + -2 = 15.435595774
t = 15.435595774

Simplifying
t = 15.435595774

Subproblem 2
t + 2 = -17.435595774

Simplifying
t + 2 = -17.435595774

Reorder the terms:
2 + t = -17.435595774

Solving
2 + t = -17.435595774

Solving for variable 't'.

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

Add '-2' to each side of the equation.
2 + -2 + t = -17.435595774 + -2

Combine like terms: 2 + -2 = 0
0 + t = -17.435595774 + -2
t = -17.435595774 + -2

Combine like terms: -17.435595774 + -2 = -19.435595774
t = -19.435595774

Simplifying
t = -19.435595774

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {15.435595774, -19.435595774}