-3x^2-14x+15=0

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Solution for -3x^2-14x+15=0 equation: 


Simplifying
-3x2 + -14x + 15 = 0

Reorder the terms:
15 + -14x + -3x2 = 0

Solving
15 + -14x + -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'.
-5 + 4.666666667x + x2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 4.666666667x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + 4.666666667x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 4.666666667x + x2 = 0 + 5
4.666666667x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
4.666666667x + x2 = 5

The x term is 4.666666667x.  Take half its coefficient (2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
4.666666667x + 5.444444448 + x2 = 5 + 5.444444448

Reorder the terms:
5.444444448 + 4.666666667x + x2 = 5 + 5.444444448

Combine like terms: 5 + 5.444444448 = 10.444444448
5.444444448 + 4.666666667x + x2 = 10.444444448

Factor a perfect square on the left side:
(x + 2.333333334)(x + 2.333333334) = 10.444444448

Calculate the square root of the right side: 3.231786572

Break this problem into two subproblems by setting 
(x + 2.333333334) equal to 3.231786572 and -3.231786572.


Subproblem 1
x + 2.333333334 = 3.231786572

Simplifying
x + 2.333333334 = 3.231786572

Reorder the terms:
2.333333334 + x = 3.231786572

Solving
2.333333334 + x = 3.231786572

Solving for variable 'x'.

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

Add '-2.333333334' to each side of the equation.
2.333333334 + -2.333333334 + x = 3.231786572 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + x = 3.231786572 + -2.333333334
x = 3.231786572 + -2.333333334

Combine like terms: 3.231786572 + -2.333333334 = 0.898453238
x = 0.898453238

Simplifying
x = 0.898453238


Subproblem 2
x + 2.333333334 = -3.231786572

Simplifying
x + 2.333333334 = -3.231786572

Reorder the terms:
2.333333334 + x = -3.231786572

Solving
2.333333334 + x = -3.231786572

Solving for variable 'x'.

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

Add '-2.333333334' to each side of the equation.
2.333333334 + -2.333333334 + x = -3.231786572 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + x = -3.231786572 + -2.333333334
x = -3.231786572 + -2.333333334

Combine like terms: -3.231786572 + -2.333333334 = -5.565119906
x = -5.565119906

Simplifying
x = -5.565119906


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.898453238, -5.565119906}

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