here see wolfarm
15 min. is nothing! What is the original problem?
1.025^n=0.71+0.05n - Wolfram|Alpha
First off, your post title is misleading. This equation is exponential, not quadratic.
Note that elementary algebraic methods will not work in finding a solution by hand.
I advise the use of technology to solve the equation. Another poster has provided you a link to that end.
May I ask why you title this "Solving quadratic equations"? This is certainly not a quadratic equation. It is not even a polynomial equation.
The point the others are making is that there is no simple formula that will give you an exact answer. Probably the simplest thing to do is to graph y= 1.025^n and y= 0.71+ .05n on some kind of calculator or computer graphics system and "zoom" in on a point where they intersect.
You could also use some kind of numerical method such as Newton's method to find a numerical problem.