28x^2=11x-1

Solution for 28x^2=11x-1 equation:

Simplifying
28x2 = 11x + -1

Reorder the terms:
28x2 = -1 + 11x

Solving
28x2 = -1 + 11x

Solving for variable 'x'.

Reorder the terms:
1 + -11x + 28x2 = -1 + 11x + 1 + -11x

Reorder the terms:
1 + -11x + 28x2 = -1 + 1 + 11x + -11x

Combine like terms: -1 + 1 = 0
1 + -11x + 28x2 = 0 + 11x + -11x
1 + -11x + 28x2 = 11x + -11x

Combine like terms: 11x + -11x = 0
1 + -11x + 28x2 = 0

Factor a trinomial.
(1 + -7x)(1 + -4x) = 0

Subproblem 1
Set the factor '(1 + -7x)' equal to zero and attempt to solve:

Simplifying
1 + -7x = 0

Solving
1 + -7x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -7x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -7x = 0 + -1
-7x = 0 + -1

Combine like terms: 0 + -1 = -1
-7x = -1

Divide each side by '-7'.
x = 0.1428571429

Simplifying
x = 0.1428571429
Subproblem 2
Set the factor '(1 + -4x)' equal to zero and attempt to solve:

Simplifying
1 + -4x = 0

Solving
1 + -4x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4x = 0 + -1
-4x = 0 + -1

Combine like terms: 0 + -1 = -1
-4x = -1

Divide each side by '-4'.
x = 0.25

Simplifying
x = 0.25
Solution
x = {0.1428571429, 0.25}