2x^2-20x+37.5=0

Solution for 2x^2-20x+37.5=0 equation:

Simplifying
2x2 + -20x + 37.5 = 0

Reorder the terms:
37.5 + -20x + 2x2 = 0

Solving
37.5 + -20x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
18.75 + -10x + x2 = 0

Move the constant term to the right:

Add '-18.75' to each side of the equation.
18.75 + -10x + -18.75 + x2 = 0 + -18.75

Reorder the terms:
18.75 + -18.75 + -10x + x2 = 0 + -18.75

Combine like terms: 18.75 + -18.75 = 0.00
0.00 + -10x + x2 = 0 + -18.75
-10x + x2 = 0 + -18.75

Combine like terms: 0 + -18.75 = -18.75
-10x + x2 = -18.75

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = -18.75 + 25

Reorder the terms:
25 + -10x + x2 = -18.75 + 25

Combine like terms: -18.75 + 25 = 6.25
25 + -10x + x2 = 6.25

Factor a perfect square on the left side:
(x + -5)(x + -5) = 6.25

Calculate the square root of the right side: 2.5

Break this problem into two subproblems by setting 
(x + -5) equal to 2.5 and -2.5.

Subproblem 1
x + -5 = 2.5

Simplifying
x + -5 = 2.5

Reorder the terms:
-5 + x = 2.5

Solving
-5 + x = 2.5

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 2.5 + 5

Combine like terms: -5 + 5 = 0
0 + x = 2.5 + 5
x = 2.5 + 5

Combine like terms: 2.5 + 5 = 7.5
x = 7.5

Simplifying
x = 7.5

Subproblem 2
x + -5 = -2.5

Simplifying
x + -5 = -2.5

Reorder the terms:
-5 + x = -2.5

Solving
-5 + x = -2.5

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -2.5 + 5

Combine like terms: -5 + 5 = 0
0 + x = -2.5 + 5
x = -2.5 + 5

Combine like terms: -2.5 + 5 = 2.5
x = 2.5

Simplifying
x = 2.5

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.5, 2.5}