Ive for \( x \) leaving answers roun \[ x-3=\frac{18}{x} \]

To solve the equation \( x - 3 = \frac{18}{x} \), first multiply both sides by \( x \) to eliminate the fraction, giving you \( x^2 - 3x = 18 \). Rearranging this, you end up with the quadratic equation \( x^2 - 3x - 18 = 0 \). You can solve it using the quadratic formula, \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \). For your equation, \( a = 1, b = -3, c = -18 \), so substituting these values gives you \( x = \frac{3 \pm \sqrt{(-3)^2 - 4(1)(-18)}}{2(1)} \). Simplifying further, you'll obtain \( x = \frac{3 \pm \sqrt{81}}{2} \). Thus, your solutions are \( x = 9 \) and \( x = -2 \). Rounding them as necessary depends on the context! When handling algebraic fractions, it's essential to remember to check for extraneous solutions. For example, if one possible answer is zero or leads to a division by zero in the original equation, it must be discarded. Also, when solving quadratics, being familiar with factoring can save time, and it's a fun challenge for math lovers!