3x^2+19x-20=0

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Solution for 3x^2+19x-20=0 equation: 


Simplifying
3x2 + 19x + -20 = 0

Reorder the terms:
-20 + 19x + 3x2 = 0

Solving
-20 + 19x + 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 + 6.333333333x + x2 = 0

Move the constant term to the right:

Add '6.666666667' to each side of the equation.
-6.666666667 + 6.333333333x + 6.666666667 + x2 = 0 + 6.666666667

Reorder the terms:
-6.666666667 + 6.666666667 + 6.333333333x + x2 = 0 + 6.666666667

Combine like terms: -6.666666667 + 6.666666667 = 0.000000000
0.000000000 + 6.333333333x + x2 = 0 + 6.666666667
6.333333333x + x2 = 0 + 6.666666667

Combine like terms: 0 + 6.666666667 = 6.666666667
6.333333333x + x2 = 6.666666667

The x term is 6.333333333x.  Take half its coefficient (3.166666667).
Square it (10.02777778) and add it to both sides.

Add '10.02777778' to each side of the equation.
6.333333333x + 10.02777778 + x2 = 6.666666667 + 10.02777778

Reorder the terms:
10.02777778 + 6.333333333x + x2 = 6.666666667 + 10.02777778

Combine like terms: 6.666666667 + 10.02777778 = 16.694444447
10.02777778 + 6.333333333x + x2 = 16.694444447

Factor a perfect square on the left side:
(x + 3.166666667)(x + 3.166666667) = 16.694444447

Calculate the square root of the right side: 4.085883558

Break this problem into two subproblems by setting 
(x + 3.166666667) equal to 4.085883558 and -4.085883558.


Subproblem 1
x + 3.166666667 = 4.085883558

Simplifying
x + 3.166666667 = 4.085883558

Reorder the terms:
3.166666667 + x = 4.085883558

Solving
3.166666667 + x = 4.085883558

Solving for variable 'x'.

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

Add '-3.166666667' to each side of the equation.
3.166666667 + -3.166666667 + x = 4.085883558 + -3.166666667

Combine like terms: 3.166666667 + -3.166666667 = 0.000000000
0.000000000 + x = 4.085883558 + -3.166666667
x = 4.085883558 + -3.166666667

Combine like terms: 4.085883558 + -3.166666667 = 0.919216891
x = 0.919216891

Simplifying
x = 0.919216891


Subproblem 2
x + 3.166666667 = -4.085883558

Simplifying
x + 3.166666667 = -4.085883558

Reorder the terms:
3.166666667 + x = -4.085883558

Solving
3.166666667 + x = -4.085883558

Solving for variable 'x'.

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

Add '-3.166666667' to each side of the equation.
3.166666667 + -3.166666667 + x = -4.085883558 + -3.166666667

Combine like terms: 3.166666667 + -3.166666667 = 0.000000000
0.000000000 + x = -4.085883558 + -3.166666667
x = -4.085883558 + -3.166666667

Combine like terms: -4.085883558 + -3.166666667 = -7.252550225
x = -7.252550225

Simplifying
x = -7.252550225


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.919216891, -7.252550225}

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