To find the solutions to the equation \( 8x^2 - 2x - 3 = 0 \), we can use the quadratic formula:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
where \( a = 8 \), \( b = -2 \), and \( c = -3 \).
First, calculate the discriminant:
\[ b^2 - 4ac = (-2)^2 - 4(8)(-3) = 4 + 96 = 100 \]
Now, plug the values into the quadratic formula:
\[ x = \frac{-(-2) \pm \sqrt{100}}{2 \cdot 8} \]
This simplifies to:
\[ x = \frac{2 \pm 10}{16} \]
Now, calculate the two potential solutions:
- \( x = \frac{12}{16} = \frac{3}{4} = 0.75 \)
- \( x = \frac{-8}{16} = -0.5 \)
The solution \( x = -0.5 \) is one of the options provided:
b. -0.5
Thus, the correct answer is b. -0.5.