3x^2+48x-20=0

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Solution for 3x^2+48x-20=0 equation: 


Simplifying
3x2 + 48x + -20 = 0

Reorder the terms:
-20 + 48x + 3x2 = 0

Solving
-20 + 48x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-6.666666667 + 16x + x2 = 0

Move the constant term to the right:

Add '6.666666667' to each side of the equation.
-6.666666667 + 16x + 6.666666667 + x2 = 0 + 6.666666667

Reorder the terms:
-6.666666667 + 6.666666667 + 16x + x2 = 0 + 6.666666667

Combine like terms: -6.666666667 + 6.666666667 = 0.000000000
0.000000000 + 16x + x2 = 0 + 6.666666667
16x + x2 = 0 + 6.666666667

Combine like terms: 0 + 6.666666667 = 6.666666667
16x + x2 = 6.666666667

The x term is 16x.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16x + 64 + x2 = 6.666666667 + 64

Reorder the terms:
64 + 16x + x2 = 6.666666667 + 64

Combine like terms: 6.666666667 + 64 = 70.666666667
64 + 16x + x2 = 70.666666667

Factor a perfect square on the left side:
(x + 8)(x + 8) = 70.666666667

Calculate the square root of the right side: 8.406346809

Break this problem into two subproblems by setting 
(x + 8) equal to 8.406346809 and -8.406346809.


Subproblem 1
x + 8 = 8.406346809

Simplifying
x + 8 = 8.406346809

Reorder the terms:
8 + x = 8.406346809

Solving
8 + x = 8.406346809

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = 8.406346809 + -8

Combine like terms: 8 + -8 = 0
0 + x = 8.406346809 + -8
x = 8.406346809 + -8

Combine like terms: 8.406346809 + -8 = 0.406346809
x = 0.406346809

Simplifying
x = 0.406346809


Subproblem 2
x + 8 = -8.406346809

Simplifying
x + 8 = -8.406346809

Reorder the terms:
8 + x = -8.406346809

Solving
8 + x = -8.406346809

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = -8.406346809 + -8

Combine like terms: 8 + -8 = 0
0 + x = -8.406346809 + -8
x = -8.406346809 + -8

Combine like terms: -8.406346809 + -8 = -16.406346809
x = -16.406346809

Simplifying
x = -16.406346809


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.406346809, -16.406346809}

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