5x^2+21x-18=0

Solution for 5x^2+21x-18=0 equation:

Simplifying
5x2 + 21x + -18 = 0

Reorder the terms:
-18 + 21x + 5x2 = 0

Solving
-18 + 21x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
-3.6 + 4.2x + x2 = 0

Move the constant term to the right:

Add '3.6' to each side of the equation.
-3.6 + 4.2x + 3.6 + x2 = 0 + 3.6

Reorder the terms:
-3.6 + 3.6 + 4.2x + x2 = 0 + 3.6

Combine like terms: -3.6 + 3.6 = 0.0
0.0 + 4.2x + x2 = 0 + 3.6
4.2x + x2 = 0 + 3.6

Combine like terms: 0 + 3.6 = 3.6
4.2x + x2 = 3.6

The x term is 4.2x.  Take half its coefficient (2.1).
Square it (4.41) and add it to both sides.

Add '4.41' to each side of the equation.
4.2x + 4.41 + x2 = 3.6 + 4.41

Reorder the terms:
4.41 + 4.2x + x2 = 3.6 + 4.41

Combine like terms: 3.6 + 4.41 = 8.01
4.41 + 4.2x + x2 = 8.01

Factor a perfect square on the left side:
(x + 2.1)(x + 2.1) = 8.01

Calculate the square root of the right side: 2.83019434

Break this problem into two subproblems by setting 
(x + 2.1) equal to 2.83019434 and -2.83019434.

Subproblem 1
x + 2.1 = 2.83019434

Simplifying
x + 2.1 = 2.83019434

Reorder the terms:
2.1 + x = 2.83019434

Solving
2.1 + x = 2.83019434

Solving for variable 'x'.

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

Add '-2.1' to each side of the equation.
2.1 + -2.1 + x = 2.83019434 + -2.1

Combine like terms: 2.1 + -2.1 = 0.0
0.0 + x = 2.83019434 + -2.1
x = 2.83019434 + -2.1

Combine like terms: 2.83019434 + -2.1 = 0.73019434
x = 0.73019434

Simplifying
x = 0.73019434

Subproblem 2
x + 2.1 = -2.83019434

Simplifying
x + 2.1 = -2.83019434

Reorder the terms:
2.1 + x = -2.83019434

Solving
2.1 + x = -2.83019434

Solving for variable 'x'.

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

Add '-2.1' to each side of the equation.
2.1 + -2.1 + x = -2.83019434 + -2.1

Combine like terms: 2.1 + -2.1 = 0.0
0.0 + x = -2.83019434 + -2.1
x = -2.83019434 + -2.1

Combine like terms: -2.83019434 + -2.1 = -4.93019434
x = -4.93019434

Simplifying
x = -4.93019434

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.73019434, -4.93019434}