4.8t^2+7t-20=0

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Solution for 4.8t^2+7t-20=0 equation: 


Simplifying
4.8t2 + 7t + -20 = 0

Reorder the terms:
-20 + 7t + 4.8t2 = 0

Solving
-20 + 7t + 4.8t2 = 0

Solving for variable 't'.

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

Divide each side by '4.8'.
-4.166666667 + 1.458333333t + t2 = 0

Move the constant term to the right:

Add '4.166666667' to each side of the equation.
-4.166666667 + 1.458333333t + 4.166666667 + t2 = 0 + 4.166666667

Reorder the terms:
-4.166666667 + 4.166666667 + 1.458333333t + t2 = 0 + 4.166666667

Combine like terms: -4.166666667 + 4.166666667 = 0.000000000
0.000000000 + 1.458333333t + t2 = 0 + 4.166666667
1.458333333t + t2 = 0 + 4.166666667

Combine like terms: 0 + 4.166666667 = 4.166666667
1.458333333t + t2 = 4.166666667

The t term is 1.458333333t.  Take half its coefficient (0.7291666665).
Square it (0.5316840275) and add it to both sides.

Add '0.5316840275' to each side of the equation.
1.458333333t + 0.5316840275 + t2 = 4.166666667 + 0.5316840275

Reorder the terms:
0.5316840275 + 1.458333333t + t2 = 4.166666667 + 0.5316840275

Combine like terms: 4.166666667 + 0.5316840275 = 4.6983506945
0.5316840275 + 1.458333333t + t2 = 4.6983506945

Factor a perfect square on the left side:
(t + 0.7291666665)(t + 0.7291666665) = 4.6983506945

Calculate the square root of the right side: 2.167567922

Break this problem into two subproblems by setting 
(t + 0.7291666665) equal to 2.167567922 and -2.167567922.


Subproblem 1
t + 0.7291666665 = 2.167567922

Simplifying
t + 0.7291666665 = 2.167567922

Reorder the terms:
0.7291666665 + t = 2.167567922

Solving
0.7291666665 + t = 2.167567922

Solving for variable 't'.

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

Add '-0.7291666665' to each side of the equation.
0.7291666665 + -0.7291666665 + t = 2.167567922 + -0.7291666665

Combine like terms: 0.7291666665 + -0.7291666665 = 0.0000000000
0.0000000000 + t = 2.167567922 + -0.7291666665
t = 2.167567922 + -0.7291666665

Combine like terms: 2.167567922 + -0.7291666665 = 1.4384012555
t = 1.4384012555

Simplifying
t = 1.4384012555


Subproblem 2
t + 0.7291666665 = -2.167567922

Simplifying
t + 0.7291666665 = -2.167567922

Reorder the terms:
0.7291666665 + t = -2.167567922

Solving
0.7291666665 + t = -2.167567922

Solving for variable 't'.

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

Add '-0.7291666665' to each side of the equation.
0.7291666665 + -0.7291666665 + t = -2.167567922 + -0.7291666665

Combine like terms: 0.7291666665 + -0.7291666665 = 0.0000000000
0.0000000000 + t = -2.167567922 + -0.7291666665
t = -2.167567922 + -0.7291666665

Combine like terms: -2.167567922 + -0.7291666665 = -2.8967345885
t = -2.8967345885

Simplifying
t = -2.8967345885


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.4384012555, -2.8967345885}

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