0=150+5.5t+0.5(9.8)t^2

Solution for 0=150+5.5t+0.5(9.8)t^2 equation:

Simplifying
0 = 150 + 5.5t + 0.5(9.8) * t2

Multiply 0.5 * 9.8
0 = 150 + 5.5t + 4.9t2

Solving
0 = 150 + 5.5t + 4.9t2

Solving for variable 't'.

Combine like terms: 0 + -150 = -150
-150 + -5.5t + -4.9t2 = 150 + 5.5t + 4.9t2 + -150 + -5.5t + -4.9t2

Reorder the terms:
-150 + -5.5t + -4.9t2 = 150 + -150 + 5.5t + -5.5t + 4.9t2 + -4.9t2

Combine like terms: 150 + -150 = 0
-150 + -5.5t + -4.9t2 = 0 + 5.5t + -5.5t + 4.9t2 + -4.9t2
-150 + -5.5t + -4.9t2 = 5.5t + -5.5t + 4.9t2 + -4.9t2

Combine like terms: 5.5t + -5.5t = 0.0
-150 + -5.5t + -4.9t2 = 0.0 + 4.9t2 + -4.9t2
-150 + -5.5t + -4.9t2 = 4.9t2 + -4.9t2

Combine like terms: 4.9t2 + -4.9t2 = 0.0
-150 + -5.5t + -4.9t2 = 0.0

Begin completing the square.  Divide all terms by
-4.9 the coefficient of the squared term: 

Divide each side by '-4.9'.
30.6122449 + 1.12244898t + t2 = 0

Move the constant term to the right:

Add '-30.6122449' to each side of the equation.
30.6122449 + 1.12244898t + -30.6122449 + t2 = 0 + -30.6122449

Reorder the terms:
30.6122449 + -30.6122449 + 1.12244898t + t2 = 0 + -30.6122449

Combine like terms: 30.6122449 + -30.6122449 = 0.0000000
0.0000000 + 1.12244898t + t2 = 0 + -30.6122449
1.12244898t + t2 = 0 + -30.6122449

Combine like terms: 0 + -30.6122449 = -30.6122449
1.12244898t + t2 = -30.6122449

The t term is 1.12244898t.  Take half its coefficient (0.56122449).
Square it (0.3149729282) and add it to both sides.

Add '0.3149729282' to each side of the equation.
1.12244898t + 0.3149729282 + t2 = -30.6122449 + 0.3149729282

Reorder the terms:
0.3149729282 + 1.12244898t + t2 = -30.6122449 + 0.3149729282

Combine like terms: -30.6122449 + 0.3149729282 = -30.2972719718
0.3149729282 + 1.12244898t + t2 = -30.2972719718

Factor a perfect square on the left side:
(t + 0.56122449)(t + 0.56122449) = -30.2972719718

Can't calculate square root of the right side.

The solution to this equation could not be determined.