3x^2-79x+20=0

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Solution for 3x^2-79x+20=0 equation: 


Simplifying
3x2 + -79x + 20 = 0

Reorder the terms:
20 + -79x + 3x2 = 0

Solving
20 + -79x + 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 + -26.33333333x + x2 = 0

Move the constant term to the right:

Add '-6.666666667' to each side of the equation.
6.666666667 + -26.33333333x + -6.666666667 + x2 = 0 + -6.666666667

Reorder the terms:
6.666666667 + -6.666666667 + -26.33333333x + x2 = 0 + -6.666666667

Combine like terms: 6.666666667 + -6.666666667 = 0.000000000
0.000000000 + -26.33333333x + x2 = 0 + -6.666666667
-26.33333333x + x2 = 0 + -6.666666667

Combine like terms: 0 + -6.666666667 = -6.666666667
-26.33333333x + x2 = -6.666666667

The x term is -26.33333333x.  Take half its coefficient (-13.16666667).
Square it (173.3611112) and add it to both sides.

Add '173.3611112' to each side of the equation.
-26.33333333x + 173.3611112 + x2 = -6.666666667 + 173.3611112

Reorder the terms:
173.3611112 + -26.33333333x + x2 = -6.666666667 + 173.3611112

Combine like terms: -6.666666667 + 173.3611112 = 166.694444533
173.3611112 + -26.33333333x + x2 = 166.694444533

Factor a perfect square on the left side:
(x + -13.16666667)(x + -13.16666667) = 166.694444533

Calculate the square root of the right side: 12.911020275

Break this problem into two subproblems by setting 
(x + -13.16666667) equal to 12.911020275 and -12.911020275.


Subproblem 1
x + -13.16666667 = 12.911020275

Simplifying
x + -13.16666667 = 12.911020275

Reorder the terms:
-13.16666667 + x = 12.911020275

Solving
-13.16666667 + x = 12.911020275

Solving for variable 'x'.

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

Add '13.16666667' to each side of the equation.
-13.16666667 + 13.16666667 + x = 12.911020275 + 13.16666667

Combine like terms: -13.16666667 + 13.16666667 = 0.00000000
0.00000000 + x = 12.911020275 + 13.16666667
x = 12.911020275 + 13.16666667

Combine like terms: 12.911020275 + 13.16666667 = 26.077686945
x = 26.077686945

Simplifying
x = 26.077686945


Subproblem 2
x + -13.16666667 = -12.911020275

Simplifying
x + -13.16666667 = -12.911020275

Reorder the terms:
-13.16666667 + x = -12.911020275

Solving
-13.16666667 + x = -12.911020275

Solving for variable 'x'.

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

Add '13.16666667' to each side of the equation.
-13.16666667 + 13.16666667 + x = -12.911020275 + 13.16666667

Combine like terms: -13.16666667 + 13.16666667 = 0.00000000
0.00000000 + x = -12.911020275 + 13.16666667
x = -12.911020275 + 13.16666667

Combine like terms: -12.911020275 + 13.16666667 = 0.255646395
x = 0.255646395

Simplifying
x = 0.255646395


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {26.077686945, 0.255646395}

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