Respuesta :

Given:

[tex]6x^2-x-15=0[/tex]

Required:

To find the solution.

Explanation:

Consider

[tex]6x^2-x-15=0[/tex]

Here

[tex]\begin{gathered} a=6 \\ b=-1 \\ c=-15 \end{gathered}[/tex][tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Here

[tex]\begin{gathered} x=\frac{-(-1)\pm\sqrt{1-4(6)(-15)}}{2(6)} \\ \\ =\frac{1\pm\sqrt{1+360}}{12} \\ \\ =\frac{1\pm\sqrt{361}}{12} \\ \\ =\frac{1\pm19}{12} \end{gathered}[/tex]

Now

[tex]\begin{gathered} x=\frac{1+19}{12} \\ \\ =\frac{20}{12} \\ \\ =\frac{5}{3} \end{gathered}[/tex]

And

[tex]\begin{gathered} x=\frac{1-19}{12} \\ \\ =-\frac{18}{12} \\ \\ =-\frac{3}{2} \\ \end{gathered}[/tex]

Final Answer:

[tex]x=\frac{5}{3},-\frac{3}{2}[/tex]