-16t^2+175t-85=0

Solution for -16t^2+175t-85=0 equation:

Simplifying
-16t2 + 175t + -85 = 0

Reorder the terms:
-85 + 175t + -16t2 = 0

Solving
-85 + 175t + -16t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
-16 the coefficient of the squared term: 

Divide each side by '-16'.
5.3125 + -10.9375t + t2 = 0

Move the constant term to the right:

Add '-5.3125' to each side of the equation.
5.3125 + -10.9375t + -5.3125 + t2 = 0 + -5.3125

Reorder the terms:
5.3125 + -5.3125 + -10.9375t + t2 = 0 + -5.3125

Combine like terms: 5.3125 + -5.3125 = 0.0000
0.0000 + -10.9375t + t2 = 0 + -5.3125
-10.9375t + t2 = 0 + -5.3125

Combine like terms: 0 + -5.3125 = -5.3125
-10.9375t + t2 = -5.3125

The t term is -10.9375t.  Take half its coefficient (-5.46875).
Square it (29.90722656) and add it to both sides.

Add '29.90722656' to each side of the equation.
-10.9375t + 29.90722656 + t2 = -5.3125 + 29.90722656

Reorder the terms:
29.90722656 + -10.9375t + t2 = -5.3125 + 29.90722656

Combine like terms: -5.3125 + 29.90722656 = 24.59472656
29.90722656 + -10.9375t + t2 = 24.59472656

Factor a perfect square on the left side:
(t + -5.46875)(t + -5.46875) = 24.59472656

Calculate the square root of the right side: 4.959307065

Break this problem into two subproblems by setting 
(t + -5.46875) equal to 4.959307065 and -4.959307065.

Subproblem 1
t + -5.46875 = 4.959307065

Simplifying
t + -5.46875 = 4.959307065

Reorder the terms:
-5.46875 + t = 4.959307065

Solving
-5.46875 + t = 4.959307065

Solving for variable 't'.

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

Add '5.46875' to each side of the equation.
-5.46875 + 5.46875 + t = 4.959307065 + 5.46875

Combine like terms: -5.46875 + 5.46875 = 0.00000
0.00000 + t = 4.959307065 + 5.46875
t = 4.959307065 + 5.46875

Combine like terms: 4.959307065 + 5.46875 = 10.428057065
t = 10.428057065

Simplifying
t = 10.428057065

Subproblem 2
t + -5.46875 = -4.959307065

Simplifying
t + -5.46875 = -4.959307065

Reorder the terms:
-5.46875 + t = -4.959307065

Solving
-5.46875 + t = -4.959307065

Solving for variable 't'.

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

Add '5.46875' to each side of the equation.
-5.46875 + 5.46875 + t = -4.959307065 + 5.46875

Combine like terms: -5.46875 + 5.46875 = 0.00000
0.00000 + t = -4.959307065 + 5.46875
t = -4.959307065 + 5.46875

Combine like terms: -4.959307065 + 5.46875 = 0.509442935
t = 0.509442935

Simplifying
t = 0.509442935

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {10.428057065, 0.509442935}