0=(-.02x^2)+1.7x+5.1

Solution for 0=(-.02x^2)+1.7x+5.1 equation:

Simplifying
0 = (-0.02x2) + 1.7x + 5.1

Reorder the terms:
0 = 5.1 + 1.7x + (-0.02x2)

Solving
0 = 5.1 + 1.7x + (-0.02x2)

Solving for variable 'x'.

Combine like terms: 0 + -5.1 = -5.1
-5.1 + -1.7x + (0.02x2) = 5.1 + 1.7x + (-0.02x2) + -5.1 + -1.7x + (0.02x2)

Reorder the terms:
-5.1 + -1.7x + (0.02x2) = 5.1 + -5.1 + 1.7x + -1.7x + (-0.02x2) + (0.02x2)

Combine like terms: 5.1 + -5.1 = 0.0
-5.1 + -1.7x + (0.02x2) = 0.0 + 1.7x + -1.7x + (-0.02x2) + (0.02x2)
-5.1 + -1.7x + (0.02x2) = 1.7x + -1.7x + (-0.02x2) + (0.02x2)

Combine like terms: 1.7x + -1.7x = 0.0
-5.1 + -1.7x + (0.02x2) = 0.0 + (-0.02x2) + (0.02x2)
-5.1 + -1.7x + (0.02x2) = (-0.02x2) + (0.02x2)

Combine like terms: (-0.02x2) + (0.02x2) = 0.00
-5.1 + -1.7x + (0.02x2) = 0.00

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

Divide each side by '0.02'.
-255 + -85x + x2 = 0

Move the constant term to the right:

Add '255' to each side of the equation.
-255 + -85x + 255 + x2 = 0 + 255

Reorder the terms:
-255 + 255 + -85x + x2 = 0 + 255

Combine like terms: -255 + 255 = 0
0 + -85x + x2 = 0 + 255
-85x + x2 = 0 + 255

Combine like terms: 0 + 255 = 255
-85x + x2 = 255

The x term is -85x.  Take half its coefficient (-42.5).
Square it (1806.25) and add it to both sides.

Add '1806.25' to each side of the equation.
-85x + 1806.25 + x2 = 255 + 1806.25

Reorder the terms:
1806.25 + -85x + x2 = 255 + 1806.25

Combine like terms: 255 + 1806.25 = 2061.25
1806.25 + -85x + x2 = 2061.25

Factor a perfect square on the left side:
((x) + -42.5)((x) + -42.5) = 2061.25

Calculate the square root of the right side: 45.400991179

Break this problem into two subproblems by setting 
((x) + -42.5) equal to 45.400991179 and -45.400991179.

Subproblem 1
(x) + -42.5 = 45.400991179

Simplifying
(x) + -42.5 = 45.400991179
x + -42.5 = 45.400991179

Reorder the terms:
-42.5 + x = 45.400991179

Solving
-42.5 + x = 45.400991179

Solving for variable 'x'.

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

Add '42.5' to each side of the equation.
-42.5 + 42.5 + x = 45.400991179 + 42.5

Combine like terms: -42.5 + 42.5 = 0.0
0.0 + x = 45.400991179 + 42.5
x = 45.400991179 + 42.5

Combine like terms: 45.400991179 + 42.5 = 87.900991179
x = 87.900991179

Simplifying
x = 87.900991179

Subproblem 2
(x) + -42.5 = -45.400991179

Simplifying
(x) + -42.5 = -45.400991179
x + -42.5 = -45.400991179

Reorder the terms:
-42.5 + x = -45.400991179

Solving
-42.5 + x = -45.400991179

Solving for variable 'x'.

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

Add '42.5' to each side of the equation.
-42.5 + 42.5 + x = -45.400991179 + 42.5

Combine like terms: -42.5 + 42.5 = 0.0
0.0 + x = -45.400991179 + 42.5
x = -45.400991179 + 42.5

Combine like terms: -45.400991179 + 42.5 = -2.900991179
x = -2.900991179

Simplifying
x = -2.900991179

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {87.900991179, -2.900991179}