3. \( 4 x^{2}+8 x+3=0 \)

To solve the equation \( 4x^2 + 8x + 3 = 0 \), you can use the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = 4 \), \( b = 8 \), and \( c = 3 \). Plugging in these values, we get \( x = \frac{-8 \pm \sqrt{8^2 - 4 \cdot 4 \cdot 3}}{2 \cdot 4} \). Simplifying, you'll find the roots of this polynomial, giving you the values of \( x \). This particular quadratic might remind you of some classic themes in literature that deal with transformation and change. Just like characters often face obstacles to overcome, solving equations takes you on a journey through numbers and variables to uncover solutions, turning abstract concepts into tangible results!