SOLUTION
From the question
[tex]2x^2-15x-8=0[/tex]To factor this we say
[tex]\begin{gathered} -8\times2x^2=-16x^2 \\ so\text{ look for two items such that their sum gives the middle item} \\ -15x,\text{ and their product gives } \\ -16x^2 \\ These\text{ are } \\ -16x+x \end{gathered}[/tex]Replacing this with the middle item and factoring we have
[tex]\begin{gathered} 2x^2-25x-8=0 \\ 2x^2-16x+x-8=0 \\ 2x(x-8)+1(x-8)=0 \\ (2x+1)(x-8)=0 \end{gathered}[/tex]Now, using the product property to solve for x, we have
[tex]\begin{gathered} (2x+1)(x-8)=0 \\ 2x+1=0 \\ 2x=-1 \\ x=-\frac{1}{2}\text{ or } \\ x-8=0 \\ x=8 \end{gathered}[/tex]Hence the answer is
[tex]x=-\frac{1}{2},x=8[/tex]