20x^2+375x-3=0

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Solution for 20x^2+375x-3=0 equation: 


Simplifying
20x2 + 375x + -3 = 0

Reorder the terms:
-3 + 375x + 20x2 = 0

Solving
-3 + 375x + 20x2 = 0

Solving for variable 'x'.

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

Divide each side by '20'.
-0.15 + 18.75x + x2 = 0

Move the constant term to the right:

Add '0.15' to each side of the equation.
-0.15 + 18.75x + 0.15 + x2 = 0 + 0.15

Reorder the terms:
-0.15 + 0.15 + 18.75x + x2 = 0 + 0.15

Combine like terms: -0.15 + 0.15 = 0.00
0.00 + 18.75x + x2 = 0 + 0.15
18.75x + x2 = 0 + 0.15

Combine like terms: 0 + 0.15 = 0.15
18.75x + x2 = 0.15

The x term is 18.75x.  Take half its coefficient (9.375).
Square it (87.890625) and add it to both sides.

Add '87.890625' to each side of the equation.
18.75x + 87.890625 + x2 = 0.15 + 87.890625

Reorder the terms:
87.890625 + 18.75x + x2 = 0.15 + 87.890625

Combine like terms: 0.15 + 87.890625 = 88.040625
87.890625 + 18.75x + x2 = 88.040625

Factor a perfect square on the left side:
(x + 9.375)(x + 9.375) = 88.040625

Calculate the square root of the right side: 9.38299659

Break this problem into two subproblems by setting 
(x + 9.375) equal to 9.38299659 and -9.38299659.


Subproblem 1
x + 9.375 = 9.38299659

Simplifying
x + 9.375 = 9.38299659

Reorder the terms:
9.375 + x = 9.38299659

Solving
9.375 + x = 9.38299659

Solving for variable 'x'.

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

Add '-9.375' to each side of the equation.
9.375 + -9.375 + x = 9.38299659 + -9.375

Combine like terms: 9.375 + -9.375 = 0.000
0.000 + x = 9.38299659 + -9.375
x = 9.38299659 + -9.375

Combine like terms: 9.38299659 + -9.375 = 0.00799659
x = 0.00799659

Simplifying
x = 0.00799659


Subproblem 2
x + 9.375 = -9.38299659

Simplifying
x + 9.375 = -9.38299659

Reorder the terms:
9.375 + x = -9.38299659

Solving
9.375 + x = -9.38299659

Solving for variable 'x'.

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

Add '-9.375' to each side of the equation.
9.375 + -9.375 + x = -9.38299659 + -9.375

Combine like terms: 9.375 + -9.375 = 0.000
0.000 + x = -9.38299659 + -9.375
x = -9.38299659 + -9.375

Combine like terms: -9.38299659 + -9.375 = -18.75799659
x = -18.75799659

Simplifying
x = -18.75799659


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.00799659, -18.75799659}

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