To solve the equation \( x(2x - 7) - 4x + 14 = 0 \), let's follow these steps:

1. Distribute \( x \) in the first term:
\[
x(2x - 7) = 2x^2 - 7x
\]

2. Substitute this back into the equation:
\[
2x^2 - 7x - 4x + 14 = 0
\]

3. Combine like terms:
\[
2x^2 - 11x + 14 = 0
\]

Now we have a quadratic equation in standard form:
\[
2x^2 - 11x + 14 = 0
\]

To solve this quadratic equation, we can use the quadratic formula:
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
where \( a = 2 \), \( b = -11 \), and \( c = 14 \).

First, calculate the discriminant (\( \Delta \)):
\[
\Delta = b^2 - 4ac = (-11)^2 - 4(2)(14) = 121 - 112 = 9
\]

Since the discriminant is positive, we have two real solutions. Now, apply the quadratic formula:
\[
x = \frac{-(-11) \pm \sqrt{9}}{2(2)} = \frac{11 \pm 3}{4}
\]

This gives us two solutions:
\[
x = \frac{11 + 3}{4} = \frac{14}{4} = \frac{7}{2}
\]
\[
x = \frac{11 - 3}{4} = \frac{8}{4} = 2
\]

Therefore, the solutions to the equation \( 2x^2 - 11x + 14 = 0 \) are:
\[
x = \frac{7}{2} \quad \text{and} \quad x = 2
\]