Factor this \( 3 x^{2}-5=14 x \)

To factor the equation \( 3x^{2} - 5 = 14x \), first, we rearrange it into standard form: \( 3x^{2} - 14x - 5 = 0 \). Next, we can use the quadratic formula, \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), with \( a = 3 \), \( b = -14 \), and \( c = -5 \). Plugging in the values, we can find the roots, which will help us express the quadratic in a factored form. Now, let’s talk about what happens when you make a common mistake. A frequent error is neglecting to set the equation to zero before trying to factor. Always ensure you're starting from standard form when attempting to solve quadratic equations – allowing for successful factoring or application of the quadratic formula!