0=14x^2+x-4

Solution for 0=14x^2+x-4 equation:

Simplifying
0 = 14x2 + x + -4

Reorder the terms:
0 = -4 + x + 14x2

Solving
0 = -4 + x + 14x2

Solving for variable 'x'.

Combine like terms: 0 + 4 = 4
4 + -1x + -14x2 = -4 + x + 14x2 + 4 + -1x + -14x2

Reorder the terms:
4 + -1x + -14x2 = -4 + 4 + x + -1x + 14x2 + -14x2

Combine like terms: -4 + 4 = 0
4 + -1x + -14x2 = 0 + x + -1x + 14x2 + -14x2
4 + -1x + -14x2 = x + -1x + 14x2 + -14x2

Combine like terms: x + -1x = 0
4 + -1x + -14x2 = 0 + 14x2 + -14x2
4 + -1x + -14x2 = 14x2 + -14x2

Combine like terms: 14x2 + -14x2 = 0
4 + -1x + -14x2 = 0

Factor a trinomial.
(1 + -2x)(4 + 7x) = 0

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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Subproblem 2
Set the factor '(4 + 7x)' equal to zero and attempt to solve:

Simplifying
4 + 7x = 0

Solving
4 + 7x = 0

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

Add '-4' to each side of the equation.
4 + -4 + 7x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 7x = 0 + -4
7x = 0 + -4

Combine like terms: 0 + -4 = -4
7x = -4

Divide each side by '7'.
x = -0.5714285714

Simplifying
x = -0.5714285714
Solution
x = {0.5, -0.5714285714}