-1000+20t+(2.5)t^2=-30t+(1.6)t^2

Solution for -1000+20t+(2.5)t^2=-30t+(1.6)t^2 equation:

Simplifying
-1000 + 20t + (2.5) * t2 = -30t + (1.6) * t2

Solving
-1000 + 20t + 2.5t2 = -30t + 1.6t2

Solving for variable 't'.

Reorder the terms:
-1000 + 20t + 30t + 2.5t2 + -1.6t2 = -30t + 1.6t2 + 30t + -1.6t2

Combine like terms: 20t + 30t = 50t
-1000 + 50t + 2.5t2 + -1.6t2 = -30t + 1.6t2 + 30t + -1.6t2

Combine like terms: 2.5t2 + -1.6t2 = 0.9t2
-1000 + 50t + 0.9t2 = -30t + 1.6t2 + 30t + -1.6t2

Reorder the terms:
-1000 + 50t + 0.9t2 = -30t + 30t + 1.6t2 + -1.6t2

Combine like terms: -30t + 30t = 0
-1000 + 50t + 0.9t2 = 0 + 1.6t2 + -1.6t2
-1000 + 50t + 0.9t2 = 1.6t2 + -1.6t2

Combine like terms: 1.6t2 + -1.6t2 = 0.0
-1000 + 50t + 0.9t2 = 0.0

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

Divide each side by '0.9'.
-1111.111111 + 55.55555556t + t2 = 0

Move the constant term to the right:

Add '1111.111111' to each side of the equation.
-1111.111111 + 55.55555556t + 1111.111111 + t2 = 0 + 1111.111111

Reorder the terms:
-1111.111111 + 1111.111111 + 55.55555556t + t2 = 0 + 1111.111111

Combine like terms: -1111.111111 + 1111.111111 = 0.000000
0.000000 + 55.55555556t + t2 = 0 + 1111.111111
55.55555556t + t2 = 0 + 1111.111111

Combine like terms: 0 + 1111.111111 = 1111.111111
55.55555556t + t2 = 1111.111111

The t term is 55.55555556t.  Take half its coefficient (27.77777778).
Square it (771.6049384) and add it to both sides.

Add '771.6049384' to each side of the equation.
55.55555556t + 771.6049384 + t2 = 1111.111111 + 771.6049384

Reorder the terms:
771.6049384 + 55.55555556t + t2 = 1111.111111 + 771.6049384

Combine like terms: 1111.111111 + 771.6049384 = 1882.7160494
771.6049384 + 55.55555556t + t2 = 1882.7160494

Factor a perfect square on the left side:
(t + 27.77777778)(t + 27.77777778) = 1882.7160494

Calculate the square root of the right side: 43.390275977

Break this problem into two subproblems by setting 
(t + 27.77777778) equal to 43.390275977 and -43.390275977.

Subproblem 1
t + 27.77777778 = 43.390275977

Simplifying
t + 27.77777778 = 43.390275977

Reorder the terms:
27.77777778 + t = 43.390275977

Solving
27.77777778 + t = 43.390275977

Solving for variable 't'.

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

Add '-27.77777778' to each side of the equation.
27.77777778 + -27.77777778 + t = 43.390275977 + -27.77777778

Combine like terms: 27.77777778 + -27.77777778 = 0.00000000
0.00000000 + t = 43.390275977 + -27.77777778
t = 43.390275977 + -27.77777778

Combine like terms: 43.390275977 + -27.77777778 = 15.612498197
t = 15.612498197

Simplifying
t = 15.612498197

Subproblem 2
t + 27.77777778 = -43.390275977

Simplifying
t + 27.77777778 = -43.390275977

Reorder the terms:
27.77777778 + t = -43.390275977

Solving
27.77777778 + t = -43.390275977

Solving for variable 't'.

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

Add '-27.77777778' to each side of the equation.
27.77777778 + -27.77777778 + t = -43.390275977 + -27.77777778

Combine like terms: 27.77777778 + -27.77777778 = 0.00000000
0.00000000 + t = -43.390275977 + -27.77777778
t = -43.390275977 + -27.77777778

Combine like terms: -43.390275977 + -27.77777778 = -71.168053757
t = -71.168053757

Simplifying
t = -71.168053757

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {15.612498197, -71.168053757}