15x^2+7x-48=0

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Solution for 15x^2+7x-48=0 equation: 


Simplifying
15x2 + 7x + -48 = 0

Reorder the terms:
-48 + 7x + 15x2 = 0

Solving
-48 + 7x + 15x2 = 0

Solving for variable 'x'.

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

Divide each side by '15'.
-3.2 + 0.4666666667x + x2 = 0

Move the constant term to the right:

Add '3.2' to each side of the equation.
-3.2 + 0.4666666667x + 3.2 + x2 = 0 + 3.2

Reorder the terms:
-3.2 + 3.2 + 0.4666666667x + x2 = 0 + 3.2

Combine like terms: -3.2 + 3.2 = 0.0
0.0 + 0.4666666667x + x2 = 0 + 3.2
0.4666666667x + x2 = 0 + 3.2

Combine like terms: 0 + 3.2 = 3.2
0.4666666667x + x2 = 3.2

The x term is 0.4666666667x.  Take half its coefficient (0.2333333334).
Square it (0.05444444448) and add it to both sides.

Add '0.05444444448' to each side of the equation.
0.4666666667x + 0.05444444448 + x2 = 3.2 + 0.05444444448

Reorder the terms:
0.05444444448 + 0.4666666667x + x2 = 3.2 + 0.05444444448

Combine like terms: 3.2 + 0.05444444448 = 3.25444444448
0.05444444448 + 0.4666666667x + x2 = 3.25444444448

Factor a perfect square on the left side:
(x + 0.2333333334)(x + 0.2333333334) = 3.25444444448

Calculate the square root of the right side: 1.804007884

Break this problem into two subproblems by setting 
(x + 0.2333333334) equal to 1.804007884 and -1.804007884.


Subproblem 1
x + 0.2333333334 = 1.804007884

Simplifying
x + 0.2333333334 = 1.804007884

Reorder the terms:
0.2333333334 + x = 1.804007884

Solving
0.2333333334 + x = 1.804007884

Solving for variable 'x'.

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

Add '-0.2333333334' to each side of the equation.
0.2333333334 + -0.2333333334 + x = 1.804007884 + -0.2333333334

Combine like terms: 0.2333333334 + -0.2333333334 = 0.0000000000
0.0000000000 + x = 1.804007884 + -0.2333333334
x = 1.804007884 + -0.2333333334

Combine like terms: 1.804007884 + -0.2333333334 = 1.5706745506
x = 1.5706745506

Simplifying
x = 1.5706745506


Subproblem 2
x + 0.2333333334 = -1.804007884

Simplifying
x + 0.2333333334 = -1.804007884

Reorder the terms:
0.2333333334 + x = -1.804007884

Solving
0.2333333334 + x = -1.804007884

Solving for variable 'x'.

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

Add '-0.2333333334' to each side of the equation.
0.2333333334 + -0.2333333334 + x = -1.804007884 + -0.2333333334

Combine like terms: 0.2333333334 + -0.2333333334 = 0.0000000000
0.0000000000 + x = -1.804007884 + -0.2333333334
x = -1.804007884 + -0.2333333334

Combine like terms: -1.804007884 + -0.2333333334 = -2.0373412174
x = -2.0373412174

Simplifying
x = -2.0373412174


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.5706745506, -2.0373412174}

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