-.02x^2+1.5x+3.4=20

Solution for -.02x^2+1.5x+3.4=20 equation:

Simplifying
-0.02x2 + 1.5x + 3.4 = 20

Reorder the terms:
3.4 + 1.5x + -0.02x2 = 20

Solving
3.4 + 1.5x + -0.02x2 = 20

Solving for variable 'x'.

Reorder the terms:
3.4 + -20 + 1.5x + -0.02x2 = 20 + -20

Combine like terms: 3.4 + -20 = -16.6
-16.6 + 1.5x + -0.02x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-16.6 + 1.5x + -0.02x2 = 0

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

Divide each side by '-0.02'.
830 + -75x + x2 = 0

Move the constant term to the right:

Add '-830' to each side of the equation.
830 + -75x + -830 + x2 = 0 + -830

Reorder the terms:
830 + -830 + -75x + x2 = 0 + -830

Combine like terms: 830 + -830 = 0
0 + -75x + x2 = 0 + -830
-75x + x2 = 0 + -830

Combine like terms: 0 + -830 = -830
-75x + x2 = -830

The x term is -75x.  Take half its coefficient (-37.5).
Square it (1406.25) and add it to both sides.

Add '1406.25' to each side of the equation.
-75x + 1406.25 + x2 = -830 + 1406.25

Reorder the terms:
1406.25 + -75x + x2 = -830 + 1406.25

Combine like terms: -830 + 1406.25 = 576.25
1406.25 + -75x + x2 = 576.25

Factor a perfect square on the left side:
(x + -37.5)(x + -37.5) = 576.25

Calculate the square root of the right side: 24.005207768

Break this problem into two subproblems by setting 
(x + -37.5) equal to 24.005207768 and -24.005207768.

Subproblem 1
x + -37.5 = 24.005207768

Simplifying
x + -37.5 = 24.005207768

Reorder the terms:
-37.5 + x = 24.005207768

Solving
-37.5 + x = 24.005207768

Solving for variable 'x'.

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

Add '37.5' to each side of the equation.
-37.5 + 37.5 + x = 24.005207768 + 37.5

Combine like terms: -37.5 + 37.5 = 0.0
0.0 + x = 24.005207768 + 37.5
x = 24.005207768 + 37.5

Combine like terms: 24.005207768 + 37.5 = 61.505207768
x = 61.505207768

Simplifying
x = 61.505207768

Subproblem 2
x + -37.5 = -24.005207768

Simplifying
x + -37.5 = -24.005207768

Reorder the terms:
-37.5 + x = -24.005207768

Solving
-37.5 + x = -24.005207768

Solving for variable 'x'.

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

Add '37.5' to each side of the equation.
-37.5 + 37.5 + x = -24.005207768 + 37.5

Combine like terms: -37.5 + 37.5 = 0.0
0.0 + x = -24.005207768 + 37.5
x = -24.005207768 + 37.5

Combine like terms: -24.005207768 + 37.5 = 13.494792232
x = 13.494792232

Simplifying
x = 13.494792232

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {61.505207768, 13.494792232}