8x2-14x+5=0

To solve the quadratic equation \( 8x^2 - 14x + 5 = 0 \), we can use the quadratic formula:

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

Here, \( a = 8 \), \( b = -14 \), and \( c = 5 \).

First, we calculate the discriminant:

\[ b^2 - 4ac = (-14)^2 - 4(8)(5) = 196 - 160 = 36 \]

Now we plug this into the quadratic formula:

\[ x = \frac{-(-14) \pm \sqrt{36}}{2(8)} = \frac{14 \pm 6}{16} \]

This gives us two potential solutions:

1. \( x = \frac{14 + 6}{16} = \frac{20}{16} = \frac{5}{4} \)
2. \( x = \frac{14 - 6}{16} = \frac{8}{16} = \frac{1}{2} \)

Thus, the solutions to the equation \( 8x^2 - 14x + 5 = 0 \) are:

\[ x = \frac{5}{4} \quad \text{and} \quad x = \frac{1}{2} \]