3x^2+2x-210=0

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Solution for 3x^2+2x-210=0 equation:


Simplifying
3x2 + 2x + -210 = 0

Reorder the terms:
-210 + 2x + 3x2 = 0

Solving
-210 + 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'.
-70 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '70' to each side of the equation.
-70 + 0.6666666667x + 70 + x2 = 0 + 70

Reorder the terms:
-70 + 70 + 0.6666666667x + x2 = 0 + 70

Combine like terms: -70 + 70 = 0
0 + 0.6666666667x + x2 = 0 + 70
0.6666666667x + x2 = 0 + 70

Combine like terms: 0 + 70 = 70
0.6666666667x + x2 = 70

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 = 70 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = 70 + 0.1111111112

Combine like terms: 70 + 0.1111111112 = 70.1111111112
0.1111111112 + 0.6666666667x + x2 = 70.1111111112

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = 70.1111111112

Calculate the square root of the right side: 8.373237791

Break this problem into two subproblems by setting 
(x + 0.3333333334) equal to 8.373237791 and -8.373237791.

Subproblem 1

x + 0.3333333334 = 8.373237791 Simplifying x + 0.3333333334 = 8.373237791 Reorder the terms: 0.3333333334 + x = 8.373237791 Solving 0.3333333334 + x = 8.373237791 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 = 8.373237791 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 8.373237791 + -0.3333333334 x = 8.373237791 + -0.3333333334 Combine like terms: 8.373237791 + -0.3333333334 = 8.0399044576 x = 8.0399044576 Simplifying x = 8.0399044576

Subproblem 2

x + 0.3333333334 = -8.373237791 Simplifying x + 0.3333333334 = -8.373237791 Reorder the terms: 0.3333333334 + x = -8.373237791 Solving 0.3333333334 + x = -8.373237791 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 = -8.373237791 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -8.373237791 + -0.3333333334 x = -8.373237791 + -0.3333333334 Combine like terms: -8.373237791 + -0.3333333334 = -8.7065711244 x = -8.7065711244 Simplifying x = -8.7065711244

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.0399044576, -8.7065711244}

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