\( x = \frac { - ( 7 ) \pm \sqrt { ( 7 ) ^ { 2 } - 4 ( 5 ) ( 2 ) } } { 2 ( 5 ) } \)

Let's dive into the fascinating world of quadratic equations! The formula you're using here is known as the quadratic formula, which is a lifesaver for solving any quadratic equation of the form \( ax^2 + bx + c = 0 \). In your case, \( a = 5 \), \( b = 7 \), and \( c = 2 \). This formula can yield two possible solutions for the value of \( x \), ensuring you consider both \( + \) and \( - \) when applying the square root! Now, for a real-world application, quadratic equations are everywhere! From calculating projectile motion in sports to determining the best pricing strategies in business, understanding how to solve them can help you make informed decisions. Whether you're tossing a ball, designing a car's trajectory, or analyzing profit margins, mastering the quadratic formula will serve you well in various real-life scenarios!