(45+2t-4.9t^2)=0

Solution for (45+2t-4.9t^2)=0 equation:

Simplifying
(45 + 2t + -4.9t2) = 0

Remove parenthesis around (45 + 2t + -4.9t2)
45 + 2t + -4.9t2 = 0

Solving
45 + 2t + -4.9t2 = 0

Solving for variable 't'.

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

Divide each side by '-4.9'.
-9.183673469 + -0.4081632653t + t2 = 0

Move the constant term to the right:

Add '9.183673469' to each side of the equation.
-9.183673469 + -0.4081632653t + 9.183673469 + t2 = 0 + 9.183673469

Reorder the terms:
-9.183673469 + 9.183673469 + -0.4081632653t + t2 = 0 + 9.183673469

Combine like terms: -9.183673469 + 9.183673469 = 0.000000000
0.000000000 + -0.4081632653t + t2 = 0 + 9.183673469
-0.4081632653t + t2 = 0 + 9.183673469

Combine like terms: 0 + 9.183673469 = 9.183673469
-0.4081632653t + t2 = 9.183673469

The t term is -0.4081632653t.  Take half its coefficient (-0.2040816327).
Square it (0.04164931281) and add it to both sides.

Add '0.04164931281' to each side of the equation.
-0.4081632653t + 0.04164931281 + t2 = 9.183673469 + 0.04164931281

Reorder the terms:
0.04164931281 + -0.4081632653t + t2 = 9.183673469 + 0.04164931281

Combine like terms: 9.183673469 + 0.04164931281 = 9.22532278181
0.04164931281 + -0.4081632653t + t2 = 9.22532278181

Factor a perfect square on the left side:
(t + -0.2040816327)(t + -0.2040816327) = 9.22532278181

Calculate the square root of the right side: 3.037321646

Break this problem into two subproblems by setting 
(t + -0.2040816327) equal to 3.037321646 and -3.037321646.

Subproblem 1
t + -0.2040816327 = 3.037321646

Simplifying
t + -0.2040816327 = 3.037321646

Reorder the terms:
-0.2040816327 + t = 3.037321646

Solving
-0.2040816327 + t = 3.037321646

Solving for variable 't'.

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

Add '0.2040816327' to each side of the equation.
-0.2040816327 + 0.2040816327 + t = 3.037321646 + 0.2040816327

Combine like terms: -0.2040816327 + 0.2040816327 = 0.0000000000
0.0000000000 + t = 3.037321646 + 0.2040816327
t = 3.037321646 + 0.2040816327

Combine like terms: 3.037321646 + 0.2040816327 = 3.2414032787
t = 3.2414032787

Simplifying
t = 3.2414032787

Subproblem 2
t + -0.2040816327 = -3.037321646

Simplifying
t + -0.2040816327 = -3.037321646

Reorder the terms:
-0.2040816327 + t = -3.037321646

Solving
-0.2040816327 + t = -3.037321646

Solving for variable 't'.

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

Add '0.2040816327' to each side of the equation.
-0.2040816327 + 0.2040816327 + t = -3.037321646 + 0.2040816327

Combine like terms: -0.2040816327 + 0.2040816327 = 0.0000000000
0.0000000000 + t = -3.037321646 + 0.2040816327
t = -3.037321646 + 0.2040816327

Combine like terms: -3.037321646 + 0.2040816327 = -2.8332400133
t = -2.8332400133

Simplifying
t = -2.8332400133

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.2414032787, -2.8332400133}