- \( 03 x^{2}+7 x+2=0 \)

To solve the quadratic equation \( 3x^{2}+7x+2=0 \), you can use the quadratic formula \( x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{2a} \), where \( a = 3, b = 7, \) and \( c = 2 \). Plugging these values into the formula, you will find the roots of the equation. After calculating, you’ll see that the discriminant is positive, indicating two real and distinct roots! Now, if you’re solving it by factoring, just remember that it's often helpful to look for two numbers that multiply to \( ac = 6 \) (i.e., \( 3 \times 2 \)) and add up to \( b = 7 \). Sometimes, it might feel like searching for a treasure; patience and practice are key!