Find the equation of the tangent line at the point (3,4)

$\displaystyle x^{2} + 2xy - y^{2} + x = 20$

$\displaystyle 2x + [(y)(2) + (2x)(y')] - 2yy' + 1 = 0$

$\displaystyle 2x + 2y + 2xy' - 2yy' + 1 = 0$

$\displaystyle 2x + 2y + y'[2x - 2y] + 1 = 0$

$\displaystyle y'[2x - 2y] = -2x - 2y - 1$

$\displaystyle y' = \dfrac{-2x - 2y - 1}{2x - 2y}$ - Did this come out right?

What now? We have two variables so how to find the slope?