140=6x^2+2x-3

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Solution for 140=6x^2+2x-3 equation:


Simplifying
140 = 6x2 + 2x + -3

Reorder the terms:
140 = -3 + 2x + 6x2

Solving
140 = -3 + 2x + 6x2

Solving for variable 'x'.

Combine like terms: 140 + 3 = 143
143 + -2x + -6x2 = -3 + 2x + 6x2 + 3 + -2x + -6x2

Reorder the terms:
143 + -2x + -6x2 = -3 + 3 + 2x + -2x + 6x2 + -6x2

Combine like terms: -3 + 3 = 0
143 + -2x + -6x2 = 0 + 2x + -2x + 6x2 + -6x2
143 + -2x + -6x2 = 2x + -2x + 6x2 + -6x2

Combine like terms: 2x + -2x = 0
143 + -2x + -6x2 = 0 + 6x2 + -6x2
143 + -2x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
143 + -2x + -6x2 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
-23.83333333 + 0.3333333333x + x2 = 0

Move the constant term to the right:

Add '23.83333333' to each side of the equation.
-23.83333333 + 0.3333333333x + 23.83333333 + x2 = 0 + 23.83333333

Reorder the terms:
-23.83333333 + 23.83333333 + 0.3333333333x + x2 = 0 + 23.83333333

Combine like terms: -23.83333333 + 23.83333333 = 0.00000000
0.00000000 + 0.3333333333x + x2 = 0 + 23.83333333
0.3333333333x + x2 = 0 + 23.83333333

Combine like terms: 0 + 23.83333333 = 23.83333333
0.3333333333x + x2 = 23.83333333

The x term is 0.3333333333x.  Take half its coefficient (0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
0.3333333333x + 0.02777777779 + x2 = 23.83333333 + 0.02777777779

Reorder the terms:
0.02777777779 + 0.3333333333x + x2 = 23.83333333 + 0.02777777779

Combine like terms: 23.83333333 + 0.02777777779 = 23.86111110779
0.02777777779 + 0.3333333333x + x2 = 23.86111110779

Factor a perfect square on the left side:
(x + 0.1666666667)(x + 0.1666666667) = 23.86111110779

Calculate the square root of the right side: 4.88478363

Break this problem into two subproblems by setting 
(x + 0.1666666667) equal to 4.88478363 and -4.88478363.

Subproblem 1

x + 0.1666666667 = 4.88478363 Simplifying x + 0.1666666667 = 4.88478363 Reorder the terms: 0.1666666667 + x = 4.88478363 Solving 0.1666666667 + x = 4.88478363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = 4.88478363 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = 4.88478363 + -0.1666666667 x = 4.88478363 + -0.1666666667 Combine like terms: 4.88478363 + -0.1666666667 = 4.7181169633 x = 4.7181169633 Simplifying x = 4.7181169633

Subproblem 2

x + 0.1666666667 = -4.88478363 Simplifying x + 0.1666666667 = -4.88478363 Reorder the terms: 0.1666666667 + x = -4.88478363 Solving 0.1666666667 + x = -4.88478363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = -4.88478363 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = -4.88478363 + -0.1666666667 x = -4.88478363 + -0.1666666667 Combine like terms: -4.88478363 + -0.1666666667 = -5.0514502967 x = -5.0514502967 Simplifying x = -5.0514502967

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.7181169633, -5.0514502967}

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