20=5t^2-30t-45

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Solution for 20=5t^2-30t-45 equation: 


Simplifying
20 = 5t2 + -30t + -45

Reorder the terms:
20 = -45 + -30t + 5t2

Solving
20 = -45 + -30t + 5t2

Solving for variable 't'.

Combine like terms: 20 + 45 = 65
65 + 30t + -5t2 = -45 + -30t + 5t2 + 45 + 30t + -5t2

Reorder the terms:
65 + 30t + -5t2 = -45 + 45 + -30t + 30t + 5t2 + -5t2

Combine like terms: -45 + 45 = 0
65 + 30t + -5t2 = 0 + -30t + 30t + 5t2 + -5t2
65 + 30t + -5t2 = -30t + 30t + 5t2 + -5t2

Combine like terms: -30t + 30t = 0
65 + 30t + -5t2 = 0 + 5t2 + -5t2
65 + 30t + -5t2 = 5t2 + -5t2

Combine like terms: 5t2 + -5t2 = 0
65 + 30t + -5t2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(13 + 6t + -1t2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(13 + 6t + -1t2)' equal to zero and attempt to solve:

Simplifying
13 + 6t + -1t2 = 0

Solving
13 + 6t + -1t2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-13 + -6t + t2 = 0

Move the constant term to the right:

Add '13' to each side of the equation.
-13 + -6t + 13 + t2 = 0 + 13

Reorder the terms:
-13 + 13 + -6t + t2 = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -6t + t2 = 0 + 13
-6t + t2 = 0 + 13

Combine like terms: 0 + 13 = 13
-6t + t2 = 13

The t term is -6t.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6t + 9 + t2 = 13 + 9

Reorder the terms:
9 + -6t + t2 = 13 + 9

Combine like terms: 13 + 9 = 22
9 + -6t + t2 = 22

Factor a perfect square on the left side:
(t + -3)(t + -3) = 22

Calculate the square root of the right side: 4.69041576

Break this problem into two subproblems by setting 
(t + -3) equal to 4.69041576 and -4.69041576.


Subproblem 1
t + -3 = 4.69041576

Simplifying
t + -3 = 4.69041576

Reorder the terms:
-3 + t = 4.69041576

Solving
-3 + t = 4.69041576

Solving for variable 't'.

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

Add '3' to each side of the equation.
-3 + 3 + t = 4.69041576 + 3

Combine like terms: -3 + 3 = 0
0 + t = 4.69041576 + 3
t = 4.69041576 + 3

Combine like terms: 4.69041576 + 3 = 7.69041576
t = 7.69041576

Simplifying
t = 7.69041576


Subproblem 2
t + -3 = -4.69041576

Simplifying
t + -3 = -4.69041576

Reorder the terms:
-3 + t = -4.69041576

Solving
-3 + t = -4.69041576

Solving for variable 't'.

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

Add '3' to each side of the equation.
-3 + 3 + t = -4.69041576 + 3

Combine like terms: -3 + 3 = 0
0 + t = -4.69041576 + 3
t = -4.69041576 + 3

Combine like terms: -4.69041576 + 3 = -1.69041576
t = -1.69041576

Simplifying
t = -1.69041576


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {7.69041576, -1.69041576}
Solution
t = {7.69041576, -1.69041576}

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