5t^2+4t-80=0

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Solution for 5t^2+4t-80=0 equation: 


Simplifying
5t2 + 4t + -80 = 0

Reorder the terms:
-80 + 4t + 5t2 = 0

Solving
-80 + 4t + 5t2 = 0

Solving for variable 't'.

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

Divide each side by '5'.
-16 + 0.8t + t2 = 0

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 0.8t + 16 + t2 = 0 + 16

Reorder the terms:
-16 + 16 + 0.8t + t2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 0.8t + t2 = 0 + 16
0.8t + t2 = 0 + 16

Combine like terms: 0 + 16 = 16
0.8t + t2 = 16

The t term is 0.8t.  Take half its coefficient (0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
0.8t + 0.16 + t2 = 16 + 0.16

Reorder the terms:
0.16 + 0.8t + t2 = 16 + 0.16

Combine like terms: 16 + 0.16 = 16.16
0.16 + 0.8t + t2 = 16.16

Factor a perfect square on the left side:
(t + 0.4)(t + 0.4) = 16.16

Calculate the square root of the right side: 4.019950248

Break this problem into two subproblems by setting 
(t + 0.4) equal to 4.019950248 and -4.019950248.


Subproblem 1
t + 0.4 = 4.019950248

Simplifying
t + 0.4 = 4.019950248

Reorder the terms:
0.4 + t = 4.019950248

Solving
0.4 + t = 4.019950248

Solving for variable 't'.

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

Add '-0.4' to each side of the equation.
0.4 + -0.4 + t = 4.019950248 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + t = 4.019950248 + -0.4
t = 4.019950248 + -0.4

Combine like terms: 4.019950248 + -0.4 = 3.619950248
t = 3.619950248

Simplifying
t = 3.619950248


Subproblem 2
t + 0.4 = -4.019950248

Simplifying
t + 0.4 = -4.019950248

Reorder the terms:
0.4 + t = -4.019950248

Solving
0.4 + t = -4.019950248

Solving for variable 't'.

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

Add '-0.4' to each side of the equation.
0.4 + -0.4 + t = -4.019950248 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + t = -4.019950248 + -0.4
t = -4.019950248 + -0.4

Combine like terms: -4.019950248 + -0.4 = -4.419950248
t = -4.419950248

Simplifying
t = -4.419950248


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.619950248, -4.419950248}

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