3x^2+2x-60=0

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Solution for 3x^2+2x-60=0 equation: 


Simplifying
3x2 + 2x + -60 = 0

Reorder the terms:
-60 + 2x + 3x2 = 0

Solving
-60 + 2x + 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'.
-20 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + 0.6666666667x + 20 + x2 = 0 + 20

Reorder the terms:
-20 + 20 + 0.6666666667x + x2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + 0.6666666667x + x2 = 0 + 20
0.6666666667x + x2 = 0 + 20

Combine like terms: 0 + 20 = 20
0.6666666667x + x2 = 20

The x term is 0.6666666667x.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667x + 0.1111111112 + x2 = 20 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = 20 + 0.1111111112

Combine like terms: 20 + 0.1111111112 = 20.1111111112
0.1111111112 + 0.6666666667x + x2 = 20.1111111112

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = 20.1111111112

Calculate the square root of the right side: 4.484541349

Break this problem into two subproblems by setting 
(x + 0.3333333334) equal to 4.484541349 and -4.484541349.


Subproblem 1
x + 0.3333333334 = 4.484541349

Simplifying
x + 0.3333333334 = 4.484541349

Reorder the terms:
0.3333333334 + x = 4.484541349

Solving
0.3333333334 + x = 4.484541349

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = 4.484541349 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = 4.484541349 + -0.3333333334
x = 4.484541349 + -0.3333333334

Combine like terms: 4.484541349 + -0.3333333334 = 4.1512080156
x = 4.1512080156

Simplifying
x = 4.1512080156


Subproblem 2
x + 0.3333333334 = -4.484541349

Simplifying
x + 0.3333333334 = -4.484541349

Reorder the terms:
0.3333333334 + x = -4.484541349

Solving
0.3333333334 + x = -4.484541349

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = -4.484541349 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = -4.484541349 + -0.3333333334
x = -4.484541349 + -0.3333333334

Combine like terms: -4.484541349 + -0.3333333334 = -4.8178746824
x = -4.8178746824

Simplifying
x = -4.8178746824


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.1512080156, -4.8178746824}

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