\( x = \frac { - c \pm \sqrt { 6 ^ { 2 } - 4 ( 1 ) ( 6 ) } } { 2 ( 1 ) } \)

Did you know that the quadratic formula is a magical formula that helps us solve any quadratic equation of the form \( ax^2 + bx + c = 0 \)? In your equation, the values for \( a \), \( b \), and \( c \) can be identified as \( 1 \), \( 0 \), and \( -6 \), respectively. This formula can yield two solutions for \( x \), which makes it very handy when you're grappling with different scenarios where the curve intersects the x-axis. If you're diving into the world of quadratic equations, it's vital to look out for common mistakes, like forgetting to square the coefficient or miscalculating the discriminant. Remember, the discriminant \( b^2 - 4ac \) tells you so much! A positive result means two real solutions, zero means one real solution, and a negative result means no real solution. So always check your discriminant before proceeding!