15x^2+51x+30=0

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Solution for 15x^2+51x+30=0 equation: 


Simplifying
15x2 + 51x + 30 = 0

Reorder the terms:
30 + 51x + 15x2 = 0

Solving
30 + 51x + 15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(10 + 17x + 5x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(10 + 17x + 5x2)' equal to zero and attempt to solve:

Simplifying
10 + 17x + 5x2 = 0

Solving
10 + 17x + 5x2 = 0

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

Divide each side by '5'.
2 + 3.4x + x2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 3.4x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + 3.4x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3.4x + x2 = 0 + -2
3.4x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
3.4x + x2 = -2

The x term is 3.4x.  Take half its coefficient (1.7).
Square it (2.89) and add it to both sides.

Add '2.89' to each side of the equation.
3.4x + 2.89 + x2 = -2 + 2.89

Reorder the terms:
2.89 + 3.4x + x2 = -2 + 2.89

Combine like terms: -2 + 2.89 = 0.89
2.89 + 3.4x + x2 = 0.89

Factor a perfect square on the left side:
(x + 1.7)(x + 1.7) = 0.89

Calculate the square root of the right side: 0.943398113

Break this problem into two subproblems by setting 
(x + 1.7) equal to 0.943398113 and -0.943398113.


Subproblem 1
x + 1.7 = 0.943398113

Simplifying
x + 1.7 = 0.943398113

Reorder the terms:
1.7 + x = 0.943398113

Solving
1.7 + x = 0.943398113

Solving for variable 'x'.

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

Add '-1.7' to each side of the equation.
1.7 + -1.7 + x = 0.943398113 + -1.7

Combine like terms: 1.7 + -1.7 = 0.0
0.0 + x = 0.943398113 + -1.7
x = 0.943398113 + -1.7

Combine like terms: 0.943398113 + -1.7 = -0.756601887
x = -0.756601887

Simplifying
x = -0.756601887


Subproblem 2
x + 1.7 = -0.943398113

Simplifying
x + 1.7 = -0.943398113

Reorder the terms:
1.7 + x = -0.943398113

Solving
1.7 + x = -0.943398113

Solving for variable 'x'.

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

Add '-1.7' to each side of the equation.
1.7 + -1.7 + x = -0.943398113 + -1.7

Combine like terms: 1.7 + -1.7 = 0.0
0.0 + x = -0.943398113 + -1.7
x = -0.943398113 + -1.7

Combine like terms: -0.943398113 + -1.7 = -2.643398113
x = -2.643398113

Simplifying
x = -2.643398113


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.756601887, -2.643398113}
Solution
x = {-0.756601887, -2.643398113}

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