.75x^2-15x+72=0

Solution for .75x^2-15x+72=0 equation:

Simplifying
0.75x2 + -15x + 72 = 0

Reorder the terms:
72 + -15x + 0.75x2 = 0

Solving
72 + -15x + 0.75x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.75'.
96 + -20x + x2 = 0

Move the constant term to the right:

Add '-96' to each side of the equation.
96 + -20x + -96 + x2 = 0 + -96

Reorder the terms:
96 + -96 + -20x + x2 = 0 + -96

Combine like terms: 96 + -96 = 0
0 + -20x + x2 = 0 + -96
-20x + x2 = 0 + -96

Combine like terms: 0 + -96 = -96
-20x + x2 = -96

The x term is -20x.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20x + 100 + x2 = -96 + 100

Reorder the terms:
100 + -20x + x2 = -96 + 100

Combine like terms: -96 + 100 = 4
100 + -20x + x2 = 4

Factor a perfect square on the left side:
(x + -10)(x + -10) = 4

Calculate the square root of the right side: 2

Break this problem into two subproblems by setting 
(x + -10) equal to 2 and -2.

Subproblem 1
x + -10 = 2

Simplifying
x + -10 = 2

Reorder the terms:
-10 + x = 2

Solving
-10 + x = 2

Solving for variable 'x'.

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

Add '10' to each side of the equation.
-10 + 10 + x = 2 + 10

Combine like terms: -10 + 10 = 0
0 + x = 2 + 10
x = 2 + 10

Combine like terms: 2 + 10 = 12
x = 12

Simplifying
x = 12

Subproblem 2
x + -10 = -2

Simplifying
x + -10 = -2

Reorder the terms:
-10 + x = -2

Solving
-10 + x = -2

Solving for variable 'x'.

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

Add '10' to each side of the equation.
-10 + 10 + x = -2 + 10

Combine like terms: -10 + 10 = 0
0 + x = -2 + 10
x = -2 + 10

Combine like terms: -2 + 10 = 8
x = 8

Simplifying
x = 8

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12, 8}