How do you solve 4x - 17 = 15/x?

Solve  4x - 17 = 15/x  for x.

4x² - 17x = 15  {multiplied entire equation by x, to clear fraction}
4x² - 17x - 15 = 0  {subtracted 15 from both sides}
(4x + 3)(x - 5) = 0  {factored into two binomials}
4x + 3 = 0 or x - 5 = 0  {set each factor equal to 0}
4x = -3 or x = 5  {subtracted 3 and added 5, respectively}
x = - 3/4 or x = 5  {divided both sides by 4 in left equation}

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