3x^2+11x-15=0

Solution for 3x^2+11x-15=0 equation:

Simplifying
3x2 + 11x + -15 = 0

Reorder the terms:
-15 + 11x + 3x2 = 0

Solving
-15 + 11x + 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 + 3.666666667x + x2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 3.666666667x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + 3.666666667x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 3.666666667x + x2 = 0 + 5
3.666666667x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
3.666666667x + x2 = 5

The x term is 3.666666667x.  Take half its coefficient (1.833333334).
Square it (3.361111114) and add it to both sides.

Add '3.361111114' to each side of the equation.
3.666666667x + 3.361111114 + x2 = 5 + 3.361111114

Reorder the terms:
3.361111114 + 3.666666667x + x2 = 5 + 3.361111114

Combine like terms: 5 + 3.361111114 = 8.361111114
3.361111114 + 3.666666667x + x2 = 8.361111114

Factor a perfect square on the left side:
(x + 1.833333334)(x + 1.833333334) = 8.361111114

Calculate the square root of the right side: 2.891558596

Break this problem into two subproblems by setting 
(x + 1.833333334) equal to 2.891558596 and -2.891558596.

Subproblem 1
x + 1.833333334 = 2.891558596

Simplifying
x + 1.833333334 = 2.891558596

Reorder the terms:
1.833333334 + x = 2.891558596

Solving
1.833333334 + x = 2.891558596

Solving for variable 'x'.

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

Add '-1.833333334' to each side of the equation.
1.833333334 + -1.833333334 + x = 2.891558596 + -1.833333334

Combine like terms: 1.833333334 + -1.833333334 = 0.000000000
0.000000000 + x = 2.891558596 + -1.833333334
x = 2.891558596 + -1.833333334

Combine like terms: 2.891558596 + -1.833333334 = 1.058225262
x = 1.058225262

Simplifying
x = 1.058225262

Subproblem 2
x + 1.833333334 = -2.891558596

Simplifying
x + 1.833333334 = -2.891558596

Reorder the terms:
1.833333334 + x = -2.891558596

Solving
1.833333334 + x = -2.891558596

Solving for variable 'x'.

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

Add '-1.833333334' to each side of the equation.
1.833333334 + -1.833333334 + x = -2.891558596 + -1.833333334

Combine like terms: 1.833333334 + -1.833333334 = 0.000000000
0.000000000 + x = -2.891558596 + -1.833333334
x = -2.891558596 + -1.833333334

Combine like terms: -2.891558596 + -1.833333334 = -4.72489193
x = -4.72489193

Simplifying
x = -4.72489193

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.058225262, -4.72489193}