I'm trying to solve $7.51\tan{\theta} - 2.656(\sec{\theta})^2=0$ and the way that it's been done in my notes is by somehow changing the equation to $7.51\tan{\theta} - 2.656(\tan{\theta})^2 - 2.656=0$ then using the quadratic formula to solve it, as is shown below:
Now I understand how the quadratic formula was used but I can't understand how $7.51\tan{\theta} - 2.656(\sec{\theta})^2=0$ was changed to $7.51\tan{\theta} - 2.656(\tan{\theta})^2 - 2.656=0$.
(Note: The "$\cdots$" after $2.656$ just represents the rest of the number which I rounded to $2.656$ for the sake of the question)
It is a well known trigonometric identity that $\tan^2 x +1 =\sec^2 x$. Does that help?