-16t^2+195t-87=0

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Solution for -16t^2+195t-87=0 equation: 


Simplifying
-16t2 + 195t + -87 = 0

Reorder the terms:
-87 + 195t + -16t2 = 0

Solving
-87 + 195t + -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'.
5.4375 + -12.1875t + t2 = 0

Move the constant term to the right:

Add '-5.4375' to each side of the equation.
5.4375 + -12.1875t + -5.4375 + t2 = 0 + -5.4375

Reorder the terms:
5.4375 + -5.4375 + -12.1875t + t2 = 0 + -5.4375

Combine like terms: 5.4375 + -5.4375 = 0.0000
0.0000 + -12.1875t + t2 = 0 + -5.4375
-12.1875t + t2 = 0 + -5.4375

Combine like terms: 0 + -5.4375 = -5.4375
-12.1875t + t2 = -5.4375

The t term is -12.1875t.  Take half its coefficient (-6.09375).
Square it (37.13378906) and add it to both sides.

Add '37.13378906' to each side of the equation.
-12.1875t + 37.13378906 + t2 = -5.4375 + 37.13378906

Reorder the terms:
37.13378906 + -12.1875t + t2 = -5.4375 + 37.13378906

Combine like terms: -5.4375 + 37.13378906 = 31.69628906
37.13378906 + -12.1875t + t2 = 31.69628906

Factor a perfect square on the left side:
(t + -6.09375)(t + -6.09375) = 31.69628906

Calculate the square root of the right side: 5.629945742

Break this problem into two subproblems by setting 
(t + -6.09375) equal to 5.629945742 and -5.629945742.


Subproblem 1
t + -6.09375 = 5.629945742

Simplifying
t + -6.09375 = 5.629945742

Reorder the terms:
-6.09375 + t = 5.629945742

Solving
-6.09375 + t = 5.629945742

Solving for variable 't'.

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

Add '6.09375' to each side of the equation.
-6.09375 + 6.09375 + t = 5.629945742 + 6.09375

Combine like terms: -6.09375 + 6.09375 = 0.00000
0.00000 + t = 5.629945742 + 6.09375
t = 5.629945742 + 6.09375

Combine like terms: 5.629945742 + 6.09375 = 11.723695742
t = 11.723695742

Simplifying
t = 11.723695742


Subproblem 2
t + -6.09375 = -5.629945742

Simplifying
t + -6.09375 = -5.629945742

Reorder the terms:
-6.09375 + t = -5.629945742

Solving
-6.09375 + t = -5.629945742

Solving for variable 't'.

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

Add '6.09375' to each side of the equation.
-6.09375 + 6.09375 + t = -5.629945742 + 6.09375

Combine like terms: -6.09375 + 6.09375 = 0.00000
0.00000 + t = -5.629945742 + 6.09375
t = -5.629945742 + 6.09375

Combine like terms: -5.629945742 + 6.09375 = 0.463804258
t = 0.463804258

Simplifying
t = 0.463804258


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {11.723695742, 0.463804258}

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