e. \( 8 x^{2}+13 x+5=0 \)

Did you know that quadratic equations like \( 8x^2 + 13x + 5 = 0 \) can be solved using the quadratic formula? This formula, \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), lets you find the values of \( x \) with just a bit of algebraic magic! For your equation, plug in \( a = 8 \), \( b = 13 \), and \( c = 5 \) to discover the roots of the equation. In the real world, quadratic equations pop up in various scenarios, like when you're trying to optimize areas or determining trajectories of objects. Ever tried to calculate how high a ball will go when thrown? That involves quadratic functions! Using these equations helps to predict outcomes reliably, making them incredibly useful in both physics and engineering.