(a - 4) - a2 > 12 - 6а

To solve the inequality \((a - 4) - a^2 > 12 - 6a\), we'll first rearrange it to bring all terms to one side.

1. Start with the original inequality: \[ (a - 4) - a^2 > 12 - 6a \]

2. Rearranging gives: \[ a - 4 - a^2 - 12 + 6a > 0 \]

3. Combine like terms: \[ -a^2 + (a + 6a) - 4 - 12 > 0 \] \[ -a^2 + 7a - 16 > 0 \]

4. To make the leading term positive, we can multiply the entire inequality by -1 (remember to reverse the inequality sign): \[ a^2 - 7a + 16 < 0 \]

5. Now we need to find the roots of the quadratic equation \(a^2 - 7a + 16 = 0\) using the quadratic formula: \[ a = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] where \(a = 1\), \(b = -7\), and \(c = 16\).

   Calculate the discriminant: \[ b^2 - 4ac = (-7)^2 - 4(1)(16) = 49 - 64 = -15 \]

Since the discriminant is negative, the quadratic \(a^2 - 7a + 16\) has no real roots and is always positive (as the coefficient of \(a^2\) is positive).

Therefore, the inequality \(a^2 - 7a + 16 < 0\) has no solutions.

The conclusion is that there are no values of \(a\) that satisfy the original inequality.