Inverse of $y=2x^2-12x+13$

Question

I'm having a problem finding the inverse of $y=2x^2-12x+13$. At the end I get to the following:

$$x=3 \pm \frac{\sqrt{40+8y}}{4}$$

As far as I know the answer is suppose to be $x= 3 \pm \frac{\sqrt{y+5}}{\sqrt{2}}$ but I am unable to get to it.

Please can someone help me with the process of obtaining that answer.

Thank you

Bernard

Answer 1

$$\frac{\sqrt{40+8y}}{4} = \frac{\sqrt{8}\sqrt{5+y}}{4}= \frac{\sqrt{8}\sqrt{5+y}}{\sqrt{16}}=\frac{\sqrt{5+y}}{\sqrt{2}}$$

Answer 2

$$\sqrt{40+8y} = \sqrt{8}\sqrt{5+y}$$