(-3t^2)+30t-19=0

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Solution for (-3t^2)+30t-19=0 equation: 


Simplifying
(-3t2) + 30t + -19 = 0

Reorder the terms:
-19 + 30t + (-3t2) = 0

Solving
-19 + 30t + (-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'.
6.333333333 + -10t + t2 = 0

Move the constant term to the right:

Add '-6.333333333' to each side of the equation.
6.333333333 + -10t + -6.333333333 + t2 = 0 + -6.333333333

Reorder the terms:
6.333333333 + -6.333333333 + -10t + t2 = 0 + -6.333333333

Combine like terms: 6.333333333 + -6.333333333 = 0.000000000
0.000000000 + -10t + t2 = 0 + -6.333333333
-10t + t2 = 0 + -6.333333333

Combine like terms: 0 + -6.333333333 = -6.333333333
-10t + t2 = -6.333333333

The t term is -10t.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10t + 25 + t2 = -6.333333333 + 25

Reorder the terms:
25 + -10t + t2 = -6.333333333 + 25

Combine like terms: -6.333333333 + 25 = 18.666666667
25 + -10t + t2 = 18.666666667

Factor a perfect square on the left side:
((t) + -5)((t) + -5) = 18.666666667

Calculate the square root of the right side: 4.320493799

Break this problem into two subproblems by setting 
((t) + -5) equal to 4.320493799 and -4.320493799.


Subproblem 1
(t) + -5 = 4.320493799

Simplifying
(t) + -5 = 4.320493799
t + -5 = 4.320493799

Reorder the terms:
-5 + t = 4.320493799

Solving
-5 + t = 4.320493799

Solving for variable 't'.

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

Add '5' to each side of the equation.
-5 + 5 + t = 4.320493799 + 5

Combine like terms: -5 + 5 = 0
0 + t = 4.320493799 + 5
t = 4.320493799 + 5

Combine like terms: 4.320493799 + 5 = 9.320493799
t = 9.320493799

Simplifying
t = 9.320493799


Subproblem 2
(t) + -5 = -4.320493799

Simplifying
(t) + -5 = -4.320493799
t + -5 = -4.320493799

Reorder the terms:
-5 + t = -4.320493799

Solving
-5 + t = -4.320493799

Solving for variable 't'.

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

Add '5' to each side of the equation.
-5 + 5 + t = -4.320493799 + 5

Combine like terms: -5 + 5 = 0
0 + t = -4.320493799 + 5
t = -4.320493799 + 5

Combine like terms: -4.320493799 + 5 = 0.679506201
t = 0.679506201

Simplifying
t = 0.679506201


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {9.320493799, 0.679506201}

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