-3t^2-50t+75=0

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Solution for -3t^2-50t+75=0 equation: 


Simplifying
-3t2 + -50t + 75 = 0

Reorder the terms:
75 + -50t + -3t2 = 0

Solving
75 + -50t + -3t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-25 + 16.66666667t + t2 = 0

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + 16.66666667t + 25 + t2 = 0 + 25

Reorder the terms:
-25 + 25 + 16.66666667t + t2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + 16.66666667t + t2 = 0 + 25
16.66666667t + t2 = 0 + 25

Combine like terms: 0 + 25 = 25
16.66666667t + t2 = 25

The t term is 16.66666667t.  Take half its coefficient (8.333333335).
Square it (69.44444447) and add it to both sides.

Add '69.44444447' to each side of the equation.
16.66666667t + 69.44444447 + t2 = 25 + 69.44444447

Reorder the terms:
69.44444447 + 16.66666667t + t2 = 25 + 69.44444447

Combine like terms: 25 + 69.44444447 = 94.44444447
69.44444447 + 16.66666667t + t2 = 94.44444447

Factor a perfect square on the left side:
(t + 8.333333335)(t + 8.333333335) = 94.44444447

Calculate the square root of the right side: 9.718253159

Break this problem into two subproblems by setting 
(t + 8.333333335) equal to 9.718253159 and -9.718253159.


Subproblem 1
t + 8.333333335 = 9.718253159

Simplifying
t + 8.333333335 = 9.718253159

Reorder the terms:
8.333333335 + t = 9.718253159

Solving
8.333333335 + t = 9.718253159

Solving for variable 't'.

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

Add '-8.333333335' to each side of the equation.
8.333333335 + -8.333333335 + t = 9.718253159 + -8.333333335

Combine like terms: 8.333333335 + -8.333333335 = 0.000000000
0.000000000 + t = 9.718253159 + -8.333333335
t = 9.718253159 + -8.333333335

Combine like terms: 9.718253159 + -8.333333335 = 1.384919824
t = 1.384919824

Simplifying
t = 1.384919824


Subproblem 2
t + 8.333333335 = -9.718253159

Simplifying
t + 8.333333335 = -9.718253159

Reorder the terms:
8.333333335 + t = -9.718253159

Solving
8.333333335 + t = -9.718253159

Solving for variable 't'.

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

Add '-8.333333335' to each side of the equation.
8.333333335 + -8.333333335 + t = -9.718253159 + -8.333333335

Combine like terms: 8.333333335 + -8.333333335 = 0.000000000
0.000000000 + t = -9.718253159 + -8.333333335
t = -9.718253159 + -8.333333335

Combine like terms: -9.718253159 + -8.333333335 = -18.051586494
t = -18.051586494

Simplifying
t = -18.051586494


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.384919824, -18.051586494}

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