(20t^2+1t-6)=0

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Solution for (20t^2+1t-6)=0 equation:


Simplifying
(20t2 + 1t + -6) = 0

Reorder the terms:
(-6 + 1t + 20t2) = 0

Remove parenthesis around (-6 + 1t + 20t2)
-6 + 1t + 20t2 = 0

Solving
-6 + 1t + 20t2 = 0

Solving for variable 't'.

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

Divide each side by '20'.
-0.3 + 0.05t + t2 = 0

Move the constant term to the right:

Add '0.3' to each side of the equation.
-0.3 + 0.05t + 0.3 + t2 = 0 + 0.3

Reorder the terms:
-0.3 + 0.3 + 0.05t + t2 = 0 + 0.3

Combine like terms: -0.3 + 0.3 = 0.0
0.0 + 0.05t + t2 = 0 + 0.3
0.05t + t2 = 0 + 0.3

Combine like terms: 0 + 0.3 = 0.3
0.05t + t2 = 0.3

The t term is 0.05t.  Take half its coefficient (0.025).
Square it (0.000625) and add it to both sides.

Add '0.000625' to each side of the equation.
0.05t + 0.000625 + t2 = 0.3 + 0.000625

Reorder the terms:
0.000625 + 0.05t + t2 = 0.3 + 0.000625

Combine like terms: 0.3 + 0.000625 = 0.300625
0.000625 + 0.05t + t2 = 0.300625

Factor a perfect square on the left side:
(t + 0.025)(t + 0.025) = 0.300625

Calculate the square root of the right side: 0.548292805

Break this problem into two subproblems by setting 
(t + 0.025) equal to 0.548292805 and -0.548292805.

Subproblem 1

t + 0.025 = 0.548292805 Simplifying t + 0.025 = 0.548292805 Reorder the terms: 0.025 + t = 0.548292805 Solving 0.025 + t = 0.548292805 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.025' to each side of the equation. 0.025 + -0.025 + t = 0.548292805 + -0.025 Combine like terms: 0.025 + -0.025 = 0.000 0.000 + t = 0.548292805 + -0.025 t = 0.548292805 + -0.025 Combine like terms: 0.548292805 + -0.025 = 0.523292805 t = 0.523292805 Simplifying t = 0.523292805

Subproblem 2

t + 0.025 = -0.548292805 Simplifying t + 0.025 = -0.548292805 Reorder the terms: 0.025 + t = -0.548292805 Solving 0.025 + t = -0.548292805 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.025' to each side of the equation. 0.025 + -0.025 + t = -0.548292805 + -0.025 Combine like terms: 0.025 + -0.025 = 0.000 0.000 + t = -0.548292805 + -0.025 t = -0.548292805 + -0.025 Combine like terms: -0.548292805 + -0.025 = -0.573292805 t = -0.573292805 Simplifying t = -0.573292805

Solution

The solution to the problem is based on the solutions from the subproblems. t = {0.523292805, -0.573292805}

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