17=0.4(-9.8)t^2+10t+12

Solution for 17=0.4(-9.8)t^2+10t+12 equation:

Simplifying
17 = 0.4(-9.8) * t2 + 10t + 12

Multiply 0.4 * -9.8
17 = -3.92t2 + 10t + 12

Reorder the terms:
17 = 12 + 10t + -3.92t2

Solving
17 = 12 + 10t + -3.92t2

Solving for variable 't'.

Combine like terms: 17 + -12 = 5
5 + -10t + 3.92t2 = 12 + 10t + -3.92t2 + -12 + -10t + 3.92t2

Reorder the terms:
5 + -10t + 3.92t2 = 12 + -12 + 10t + -10t + -3.92t2 + 3.92t2

Combine like terms: 12 + -12 = 0
5 + -10t + 3.92t2 = 0 + 10t + -10t + -3.92t2 + 3.92t2
5 + -10t + 3.92t2 = 10t + -10t + -3.92t2 + 3.92t2

Combine like terms: 10t + -10t = 0
5 + -10t + 3.92t2 = 0 + -3.92t2 + 3.92t2
5 + -10t + 3.92t2 = -3.92t2 + 3.92t2

Combine like terms: -3.92t2 + 3.92t2 = 0.00
5 + -10t + 3.92t2 = 0.00

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

Divide each side by '3.92'.
1.275510204 + -2.551020408t + t2 = 0

Move the constant term to the right:

Add '-1.275510204' to each side of the equation.
1.275510204 + -2.551020408t + -1.275510204 + t2 = 0 + -1.275510204

Reorder the terms:
1.275510204 + -1.275510204 + -2.551020408t + t2 = 0 + -1.275510204

Combine like terms: 1.275510204 + -1.275510204 = 0.000000000
0.000000000 + -2.551020408t + t2 = 0 + -1.275510204
-2.551020408t + t2 = 0 + -1.275510204

Combine like terms: 0 + -1.275510204 = -1.275510204
-2.551020408t + t2 = -1.275510204

The t term is -2.551020408t.  Take half its coefficient (-1.275510204).
Square it (1.626926281) and add it to both sides.

Add '1.626926281' to each side of the equation.
-2.551020408t + 1.626926281 + t2 = -1.275510204 + 1.626926281

Reorder the terms:
1.626926281 + -2.551020408t + t2 = -1.275510204 + 1.626926281

Combine like terms: -1.275510204 + 1.626926281 = 0.351416077
1.626926281 + -2.551020408t + t2 = 0.351416077

Factor a perfect square on the left side:
(t + -1.275510204)(t + -1.275510204) = 0.351416077

Calculate the square root of the right side: 0.592803574

Break this problem into two subproblems by setting 
(t + -1.275510204) equal to 0.592803574 and -0.592803574.

Subproblem 1
t + -1.275510204 = 0.592803574

Simplifying
t + -1.275510204 = 0.592803574

Reorder the terms:
-1.275510204 + t = 0.592803574

Solving
-1.275510204 + t = 0.592803574

Solving for variable 't'.

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

Add '1.275510204' to each side of the equation.
-1.275510204 + 1.275510204 + t = 0.592803574 + 1.275510204

Combine like terms: -1.275510204 + 1.275510204 = 0.000000000
0.000000000 + t = 0.592803574 + 1.275510204
t = 0.592803574 + 1.275510204

Combine like terms: 0.592803574 + 1.275510204 = 1.868313778
t = 1.868313778

Simplifying
t = 1.868313778

Subproblem 2
t + -1.275510204 = -0.592803574

Simplifying
t + -1.275510204 = -0.592803574

Reorder the terms:
-1.275510204 + t = -0.592803574

Solving
-1.275510204 + t = -0.592803574

Solving for variable 't'.

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

Add '1.275510204' to each side of the equation.
-1.275510204 + 1.275510204 + t = -0.592803574 + 1.275510204

Combine like terms: -1.275510204 + 1.275510204 = 0.000000000
0.000000000 + t = -0.592803574 + 1.275510204
t = -0.592803574 + 1.275510204

Combine like terms: -0.592803574 + 1.275510204 = 0.68270663
t = 0.68270663

Simplifying
t = 0.68270663

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.868313778, 0.68270663}