## Answer :

1.

**Rearrange the equation:**

First, we move all terms to one side to form a standard quadratic equation:

[tex]\[ -3x^2 + 8x - 3 - 8 = 0 \][/tex]

Simplifying, we get:

[tex]\[ -3x^2 + 8x - 11 = 0 \][/tex]

2.

**Identify coefficients:**

From the quadratic equation [tex]\(ax^2 + bx + c = 0\)[/tex]:

[tex]\[ a = -3,\quad b = 8,\quad c = -11 \][/tex]

3.

**Use the quadratic formula:**

The quadratic formula is given by:

[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]

4.

**Calculate the discriminant:**

The discriminant [tex]\(\Delta\)[/tex] is calculated as follows:

[tex]\[ \Delta = b^2 - 4ac \][/tex]

Substituting the values of [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex]:

[tex]\[ \Delta = 8^2 - 4(-3)(-11) \][/tex]

Simplifying further:

[tex]\[ \Delta = 64 - 132 \][/tex]

[tex]\[ \Delta = -68 \][/tex]

Since the discriminant is negative, the solutions will be complex (imaginary).

5.

**Find the square root of the discriminant:**

The square root of the discriminant is:

[tex]\[ \sqrt{-68} = \sqrt{68}i = \sqrt{4 \cdot 17}i = 2\sqrt{17}i \][/tex]

6.

**Substitute into the quadratic formula:**

Now we substitute the values back into the quadratic formula:

[tex]\[ x = \frac{-8 \pm 2\sqrt{17}i}{2(-3)} \][/tex]

Simplify the expression:

[tex]\[ x = \frac{-8 \pm 2\sqrt{17}i}{-6} \][/tex]

Separate the real and imaginary parts:

[tex]\[ x = \frac{-8}{-6} \pm \frac{2\sqrt{17}i}{-6} \][/tex]

Simplify each part:

[tex]\[ x = \frac{4}{3} \mp \frac{\sqrt{17}i}{3} \][/tex]

7.

**Round solutions to three decimal places:**

As [tex]\(\sqrt{17} \approx 4.123\)[/tex], we get:

[tex]\[ x = \frac{4}{3} \mp \frac{4.123i}{3} \][/tex]

Simplify the final solution:

[tex]\[ x = 1.333 \mp 1.374i \][/tex]

Therefore, the solutions are:

[tex]\[ x = 1.333 + 1.374i \quad \text{and} \quad x = 1.333 - 1.374i \][/tex]

These are the rounded solutions to three decimal places.