x(2x)+1=28

Solution for x(2x)+1=28 equation:

Simplifying
x(2x) + 1 = 28

Remove parenthesis around (2x)
x * 2x + 1 = 28

Reorder the terms for easier multiplication:
2x * x + 1 = 28

Multiply x * x
2x2 + 1 = 28

Reorder the terms:
1 + 2x2 = 28

Solving
1 + 2x2 = 28

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + 2x2 = 28 + -1

Combine like terms: 1 + -1 = 0
0 + 2x2 = 28 + -1
2x2 = 28 + -1

Combine like terms: 28 + -1 = 27
2x2 = 27

Divide each side by '2'.
x2 = 13.5

Simplifying
x2 = 13.5

Take the square root of each side:
x = {-3.674234614, 3.674234614}