5+2t=12+18t-4.905t^2

Solution for 5+2t=12+18t-4.905t^2 equation:

Simplifying
5 + 2t = 12 + 18t + -4.905t2

Solving
5 + 2t = 12 + 18t + -4.905t2

Solving for variable 't'.

Reorder the terms:
5 + -12 + 2t + -18t + 4.905t2 = 12 + 18t + -4.905t2 + -12 + -18t + 4.905t2

Combine like terms: 5 + -12 = -7
-7 + 2t + -18t + 4.905t2 = 12 + 18t + -4.905t2 + -12 + -18t + 4.905t2

Combine like terms: 2t + -18t = -16t
-7 + -16t + 4.905t2 = 12 + 18t + -4.905t2 + -12 + -18t + 4.905t2

Reorder the terms:
-7 + -16t + 4.905t2 = 12 + -12 + 18t + -18t + -4.905t2 + 4.905t2

Combine like terms: 12 + -12 = 0
-7 + -16t + 4.905t2 = 0 + 18t + -18t + -4.905t2 + 4.905t2
-7 + -16t + 4.905t2 = 18t + -18t + -4.905t2 + 4.905t2

Combine like terms: 18t + -18t = 0
-7 + -16t + 4.905t2 = 0 + -4.905t2 + 4.905t2
-7 + -16t + 4.905t2 = -4.905t2 + 4.905t2

Combine like terms: -4.905t2 + 4.905t2 = 0.000
-7 + -16t + 4.905t2 = 0.000

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

Divide each side by '4.905'.
-1.427115189 + -3.261977574t + t2 = 0

Move the constant term to the right:

Add '1.427115189' to each side of the equation.
-1.427115189 + -3.261977574t + 1.427115189 + t2 = 0 + 1.427115189

Reorder the terms:
-1.427115189 + 1.427115189 + -3.261977574t + t2 = 0 + 1.427115189

Combine like terms: -1.427115189 + 1.427115189 = 0.000000000
0.000000000 + -3.261977574t + t2 = 0 + 1.427115189
-3.261977574t + t2 = 0 + 1.427115189

Combine like terms: 0 + 1.427115189 = 1.427115189
-3.261977574t + t2 = 1.427115189

The t term is -3.261977574t.  Take half its coefficient (-1.630988787).
Square it (2.660124423) and add it to both sides.

Add '2.660124423' to each side of the equation.
-3.261977574t + 2.660124423 + t2 = 1.427115189 + 2.660124423

Reorder the terms:
2.660124423 + -3.261977574t + t2 = 1.427115189 + 2.660124423

Combine like terms: 1.427115189 + 2.660124423 = 4.087239612
2.660124423 + -3.261977574t + t2 = 4.087239612

Factor a perfect square on the left side:
(t + -1.630988787)(t + -1.630988787) = 4.087239612

Calculate the square root of the right side: 2.021692264

Break this problem into two subproblems by setting 
(t + -1.630988787) equal to 2.021692264 and -2.021692264.

Subproblem 1
t + -1.630988787 = 2.021692264

Simplifying
t + -1.630988787 = 2.021692264

Reorder the terms:
-1.630988787 + t = 2.021692264

Solving
-1.630988787 + t = 2.021692264

Solving for variable 't'.

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

Add '1.630988787' to each side of the equation.
-1.630988787 + 1.630988787 + t = 2.021692264 + 1.630988787

Combine like terms: -1.630988787 + 1.630988787 = 0.000000000
0.000000000 + t = 2.021692264 + 1.630988787
t = 2.021692264 + 1.630988787

Combine like terms: 2.021692264 + 1.630988787 = 3.652681051
t = 3.652681051

Simplifying
t = 3.652681051

Subproblem 2
t + -1.630988787 = -2.021692264

Simplifying
t + -1.630988787 = -2.021692264

Reorder the terms:
-1.630988787 + t = -2.021692264

Solving
-1.630988787 + t = -2.021692264

Solving for variable 't'.

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

Add '1.630988787' to each side of the equation.
-1.630988787 + 1.630988787 + t = -2.021692264 + 1.630988787

Combine like terms: -1.630988787 + 1.630988787 = 0.000000000
0.000000000 + t = -2.021692264 + 1.630988787
t = -2.021692264 + 1.630988787

Combine like terms: -2.021692264 + 1.630988787 = -0.390703477
t = -0.390703477

Simplifying
t = -0.390703477

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.652681051, -0.390703477}