Answer:
Step-by-step explanation:
To find the solutions to the quadratic equation \( -3x^2 - 4x + 5 = 0 \) and express them in simplest radical form using the quadratic formula, we start by identifying the coefficients \( a = -3 \), \( b = -4 \), and \( c = 5 \).
The quadratic formula is:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
Substitute the values of \( a \), \( b \), and \( c \) into the formula:
\[ x = \frac{-(-4) \pm \sqrt{(-4)^2 - 4(-3)(5)}}{2(-3)} \]
Simplify the equation:
\[ x = \frac{4 \pm \sqrt{16 + 60}}{-6} \]
\[ x = \frac{4 \pm \sqrt{76}}{-6} \]
Now, simplify \( \sqrt{76} \):
\[ \sqrt{76} = \sqrt{4 \cdot 19} = 2\sqrt{19} \]
So the equation becomes:
\[ x = \frac{4 \pm 2\sqrt{19}}{-6} \]
Divide both terms in the numerator by -2:
\[ x = \frac{-2 \pm \sqrt{19}}{3} \]
Therefore, the solutions in simplest radical form are:
\[ x = \frac{-2 + \sqrt{19}}{3} \quad \text{and} \quad x = \frac{-2 - \sqrt{19}}{3} \]
Thus, the correct answer is:
\[ x = \frac{-2 \pm \sqrt{19}}{3} \]