2t^2+15t+20=0

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Solution for 2t^2+15t+20=0 equation: 


Simplifying
2t2 + 15t + 20 = 0

Reorder the terms:
20 + 15t + 2t2 = 0

Solving
20 + 15t + 2t2 = 0

Solving for variable 't'.

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

Divide each side by '2'.
10 + 7.5t + t2 = 0

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + 7.5t + -10 + t2 = 0 + -10

Reorder the terms:
10 + -10 + 7.5t + t2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 7.5t + t2 = 0 + -10
7.5t + t2 = 0 + -10

Combine like terms: 0 + -10 = -10
7.5t + t2 = -10

The t term is 7.5t.  Take half its coefficient (3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
7.5t + 14.0625 + t2 = -10 + 14.0625

Reorder the terms:
14.0625 + 7.5t + t2 = -10 + 14.0625

Combine like terms: -10 + 14.0625 = 4.0625
14.0625 + 7.5t + t2 = 4.0625

Factor a perfect square on the left side:
(t + 3.75)(t + 3.75) = 4.0625

Calculate the square root of the right side: 2.015564437

Break this problem into two subproblems by setting 
(t + 3.75) equal to 2.015564437 and -2.015564437.


Subproblem 1
t + 3.75 = 2.015564437

Simplifying
t + 3.75 = 2.015564437

Reorder the terms:
3.75 + t = 2.015564437

Solving
3.75 + t = 2.015564437

Solving for variable 't'.

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

Add '-3.75' to each side of the equation.
3.75 + -3.75 + t = 2.015564437 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + t = 2.015564437 + -3.75
t = 2.015564437 + -3.75

Combine like terms: 2.015564437 + -3.75 = -1.734435563
t = -1.734435563

Simplifying
t = -1.734435563


Subproblem 2
t + 3.75 = -2.015564437

Simplifying
t + 3.75 = -2.015564437

Reorder the terms:
3.75 + t = -2.015564437

Solving
3.75 + t = -2.015564437

Solving for variable 't'.

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

Add '-3.75' to each side of the equation.
3.75 + -3.75 + t = -2.015564437 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + t = -2.015564437 + -3.75
t = -2.015564437 + -3.75

Combine like terms: -2.015564437 + -3.75 = -5.765564437
t = -5.765564437

Simplifying
t = -5.765564437


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-1.734435563, -5.765564437}

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