-16x^2+150x-3=0

Solution for -16x^2+150x-3=0 equation:

Simplifying
-16x2 + 150x + -3 = 0

Reorder the terms:
-3 + 150x + -16x2 = 0

Solving
-3 + 150x + -16x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-16 the coefficient of the squared term: 

Divide each side by '-16'.
0.1875 + -9.375x + x2 = 0

Move the constant term to the right:

Add '-0.1875' to each side of the equation.
0.1875 + -9.375x + -0.1875 + x2 = 0 + -0.1875

Reorder the terms:
0.1875 + -0.1875 + -9.375x + x2 = 0 + -0.1875

Combine like terms: 0.1875 + -0.1875 = 0.0000
0.0000 + -9.375x + x2 = 0 + -0.1875
-9.375x + x2 = 0 + -0.1875

Combine like terms: 0 + -0.1875 = -0.1875
-9.375x + x2 = -0.1875

The x term is -9.375x.  Take half its coefficient (-4.6875).
Square it (21.97265625) and add it to both sides.

Add '21.97265625' to each side of the equation.
-9.375x + 21.97265625 + x2 = -0.1875 + 21.97265625

Reorder the terms:
21.97265625 + -9.375x + x2 = -0.1875 + 21.97265625

Combine like terms: -0.1875 + 21.97265625 = 21.78515625
21.97265625 + -9.375x + x2 = 21.78515625

Factor a perfect square on the left side:
(x + -4.6875)(x + -4.6875) = 21.78515625

Calculate the square root of the right side: 4.66745715

Break this problem into two subproblems by setting 
(x + -4.6875) equal to 4.66745715 and -4.66745715.

Subproblem 1
x + -4.6875 = 4.66745715

Simplifying
x + -4.6875 = 4.66745715

Reorder the terms:
-4.6875 + x = 4.66745715

Solving
-4.6875 + x = 4.66745715

Solving for variable 'x'.

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

Add '4.6875' to each side of the equation.
-4.6875 + 4.6875 + x = 4.66745715 + 4.6875

Combine like terms: -4.6875 + 4.6875 = 0.0000
0.0000 + x = 4.66745715 + 4.6875
x = 4.66745715 + 4.6875

Combine like terms: 4.66745715 + 4.6875 = 9.35495715
x = 9.35495715

Simplifying
x = 9.35495715

Subproblem 2
x + -4.6875 = -4.66745715

Simplifying
x + -4.6875 = -4.66745715

Reorder the terms:
-4.6875 + x = -4.66745715

Solving
-4.6875 + x = -4.66745715

Solving for variable 'x'.

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

Add '4.6875' to each side of the equation.
-4.6875 + 4.6875 + x = -4.66745715 + 4.6875

Combine like terms: -4.6875 + 4.6875 = 0.0000
0.0000 + x = -4.66745715 + 4.6875
x = -4.66745715 + 4.6875

Combine like terms: -4.66745715 + 4.6875 = 0.02004285
x = 0.02004285

Simplifying
x = 0.02004285

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.35495715, 0.02004285}