8x^2+2x-1=0

8x^2+2x-1=0    Let's see if we can factor this

(4x - 1) (2x + 1) = 0

Now, setting each factor to 0, we have

4x - 1 = 0   add 1 to both sides

4x = 1    divide by 4 on both sides

x = 1/4   and that's the first answer

And setting the other factor to 0, we have

2x + 1 =0      subtract 1 from both sides

2x = -1     divide by 2 on bith sides

x = -1/2    and that's the second answer

$$8x^2+2x-1=0$$

You need to find 2 numbers that multiply to give 8*-1=-8

They mult to give a neg so one is pos and the other is neg.

And they have to add to +2  So the biggest one will be the positive one.

The numbers are +4 and -2

Now you are going to split 2x up into 4x-2x so the equation becomes

$$8x^2+4x-2x-1=0$$

Now you can factorise the pairs like this

$$4x(2x+1)-1(2x+1)=0$$

Now factorise the LHS properly

$$(4x-1)(2x+1)=0\\
so\\
4x-1=0\qquad or \qquad 2x+1=0\\
4x=1\qquad \qquad or \qquad 2x=-1\\
x=1/4\quad \qquad or \qquad x=-1/2\\$$

OR

You could just use the quadratic formula.  

Other helpful threads:

http://web2.0calc.com/questions/grouping-method-and-factorizing-quadratic-equations

http://web2.0calc.com/questions/factorising-any-quadratic-formula-some-thoughts

http://web2.0calc.com/questions/quadratic-formula-do-you-have-trouble-remembering-it