x^2-3x-510=0

Solution for x^2-3x-510=0 equation:

Simplifying
x2 + -3x + -510 = 0

Reorder the terms:
-510 + -3x + x2 = 0

Solving
-510 + -3x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '510' to each side of the equation.
-510 + -3x + 510 + x2 = 0 + 510

Reorder the terms:
-510 + 510 + -3x + x2 = 0 + 510

Combine like terms: -510 + 510 = 0
0 + -3x + x2 = 0 + 510
-3x + x2 = 0 + 510

Combine like terms: 0 + 510 = 510
-3x + x2 = 510

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 510 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 510 + 2.25

Combine like terms: 510 + 2.25 = 512.25
2.25 + -3x + x2 = 512.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 512.25

Calculate the square root of the right side: 22.632940596

Break this problem into two subproblems by setting 
(x + -1.5) equal to 22.632940596 and -22.632940596.

Subproblem 1
x + -1.5 = 22.632940596

Simplifying
x + -1.5 = 22.632940596

Reorder the terms:
-1.5 + x = 22.632940596

Solving
-1.5 + x = 22.632940596

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 22.632940596 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 22.632940596 + 1.5
x = 22.632940596 + 1.5

Combine like terms: 22.632940596 + 1.5 = 24.132940596
x = 24.132940596

Simplifying
x = 24.132940596

Subproblem 2
x + -1.5 = -22.632940596

Simplifying
x + -1.5 = -22.632940596

Reorder the terms:
-1.5 + x = -22.632940596

Solving
-1.5 + x = -22.632940596

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -22.632940596 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -22.632940596 + 1.5
x = -22.632940596 + 1.5

Combine like terms: -22.632940596 + 1.5 = -21.132940596
x = -21.132940596

Simplifying
x = -21.132940596

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {24.132940596, -21.132940596}