[MATH] tangent problem

Let a be the x-coordinates of the pts of tangency
Let F(x) = x^2+x
F`(X) = 2x+1 F`(a) = 2a+1
The tangents are : y-(a^2+a) = (2a+1)(x-a)
y = (2a+1)x-a^2
Since the tangents pass through pt (2,-3)
-3 = 4a+2-a^2
a^2-4a-5 = 0
(a-5)(a+1) = 0
a = -1,5
When a = -1 .the tangent is : y = -x-1
When a = 5 .the tangent is : y = 11x-25