15t=-4.9t^2+32t+0.2

Solution for 15t=-4.9t^2+32t+0.2 equation:

Simplifying
15t = -4.9t2 + 32t + 0.2

Reorder the terms:
15t = 0.2 + 32t + -4.9t2

Solving
15t = 0.2 + 32t + -4.9t2

Solving for variable 't'.

Reorder the terms:
-0.2 + 15t + -32t + 4.9t2 = 0.2 + 32t + -4.9t2 + -0.2 + -32t + 4.9t2

Combine like terms: 15t + -32t = -17t
-0.2 + -17t + 4.9t2 = 0.2 + 32t + -4.9t2 + -0.2 + -32t + 4.9t2

Reorder the terms:
-0.2 + -17t + 4.9t2 = 0.2 + -0.2 + 32t + -32t + -4.9t2 + 4.9t2

Combine like terms: 0.2 + -0.2 = 0.0
-0.2 + -17t + 4.9t2 = 0.0 + 32t + -32t + -4.9t2 + 4.9t2
-0.2 + -17t + 4.9t2 = 32t + -32t + -4.9t2 + 4.9t2

Combine like terms: 32t + -32t = 0
-0.2 + -17t + 4.9t2 = 0 + -4.9t2 + 4.9t2
-0.2 + -17t + 4.9t2 = -4.9t2 + 4.9t2

Combine like terms: -4.9t2 + 4.9t2 = 0.0
-0.2 + -17t + 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'.
-0.04081632653 + -3.469387755t + t2 = 0

Move the constant term to the right:

Add '0.04081632653' to each side of the equation.
-0.04081632653 + -3.469387755t + 0.04081632653 + t2 = 0 + 0.04081632653

Reorder the terms:
-0.04081632653 + 0.04081632653 + -3.469387755t + t2 = 0 + 0.04081632653

Combine like terms: -0.04081632653 + 0.04081632653 = 0.00000000000
0.00000000000 + -3.469387755t + t2 = 0 + 0.04081632653
-3.469387755t + t2 = 0 + 0.04081632653

Combine like terms: 0 + 0.04081632653 = 0.04081632653
-3.469387755t + t2 = 0.04081632653

The t term is -3.469387755t.  Take half its coefficient (-1.734693878).
Square it (3.009162850) and add it to both sides.

Add '3.009162850' to each side of the equation.
-3.469387755t + 3.009162850 + t2 = 0.04081632653 + 3.009162850

Reorder the terms:
3.009162850 + -3.469387755t + t2 = 0.04081632653 + 3.009162850

Combine like terms: 0.04081632653 + 3.009162850 = 3.04997917653
3.009162850 + -3.469387755t + t2 = 3.04997917653

Factor a perfect square on the left side:
(t + -1.734693878)(t + -1.734693878) = 3.04997917653

Calculate the square root of the right side: 1.746418958

Break this problem into two subproblems by setting 
(t + -1.734693878) equal to 1.746418958 and -1.746418958.

Subproblem 1
t + -1.734693878 = 1.746418958

Simplifying
t + -1.734693878 = 1.746418958

Reorder the terms:
-1.734693878 + t = 1.746418958

Solving
-1.734693878 + t = 1.746418958

Solving for variable 't'.

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

Add '1.734693878' to each side of the equation.
-1.734693878 + 1.734693878 + t = 1.746418958 + 1.734693878

Combine like terms: -1.734693878 + 1.734693878 = 0.000000000
0.000000000 + t = 1.746418958 + 1.734693878
t = 1.746418958 + 1.734693878

Combine like terms: 1.746418958 + 1.734693878 = 3.481112836
t = 3.481112836

Simplifying
t = 3.481112836

Subproblem 2
t + -1.734693878 = -1.746418958

Simplifying
t + -1.734693878 = -1.746418958

Reorder the terms:
-1.734693878 + t = -1.746418958

Solving
-1.734693878 + t = -1.746418958

Solving for variable 't'.

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

Add '1.734693878' to each side of the equation.
-1.734693878 + 1.734693878 + t = -1.746418958 + 1.734693878

Combine like terms: -1.734693878 + 1.734693878 = 0.000000000
0.000000000 + t = -1.746418958 + 1.734693878
t = -1.746418958 + 1.734693878

Combine like terms: -1.746418958 + 1.734693878 = -0.01172508
t = -0.01172508

Simplifying
t = -0.01172508

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.481112836, -0.01172508}