Book Maths Puzzle Algebra

solve by suitable methods without decimals in answer

x^2+6x-8=0

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OK, I am so not worthy of your math wisdom :) (thank you for helping).
There are still a few I am lost on....I hope you have the time. :)
I am supposed to solve the equation and check for extraneous solutions:
(w-3)^1/2=(4w+15)^1/2
and
(x^2-5x+2)^1/2=x

OR

5/(y-3)=1+[(y+7)/(2y-6)]

Jon, you are helping me so much, I really do appreciate it cuz I am so lost on this stuff. Tutoring like this is my last hope. :) z(5z-1) = 3z(z+3)