how do I learned math in 1½ months

I'm taking an exam in a month and a half. Here is an old copy: http://www.studyjapan.go.jp/en/toj/pdf/013e.pdf

This is a big problem because I didn't take Algebra II in high school :( How would I go about learning this kind of stuff on the internet in a month and a half (or what are my best chances)?

Let y = 2^x.  The equation is

0 = y^2 + 2y - 15 = (y-3)(y+5)

Since 2^x > 0, 2^x = 3 and x = log(3) / log(2)