How do I find the coordinates of the two points on the curve

How do I find the coordinates of the two points on the curve y=ln(x^2+1) where the gradient is 5/13

We are given the function y = ln(x^2 +1)

We have to find the coordinates of the points where the gradient or slope is 5/13 .

To do this we first find the derivateive of y = ln(x^2 +1)

y\' = 2x / (x^2 +1)

Now as we want the slope to be 5/13

Therefore y\'= 5/13

=> 2x / (x^2 +1) = 5/13

=> 26x = 5x^2 +5

=> 5x^2 - 26 x +5 =0

=> 5x^2 -25x - x + 5 =0

=> 5x (x-5) -1(x-5) =0

=> (5x -1) (x-5) =0

=> x = 1/5 or x =5

At x= 1/5: y = ln (1/25 +1) = 0.039

At x= 5: y = ln (25+1) = 3.258.

Therefore the required points are (0.2, 0.039) and (5, 3.258)