For a general quadratic polynomial of the form:
[tex]ax^2+bx+c=0[/tex]
the solution is
[tex]x_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]
this formula is called "the quadratic formula". There are 2 solutions indicated by the subindex 1 and 2 in x.
In our case, by comparing polynomials, we can see that
[tex]\begin{gathered} a=2 \\ b=-1 \\ c=-6 \end{gathered}[/tex]
becuase our polynomial is
[tex]2x^2-x-6=0[/tex]
in which we moved 1 to the left hand side as -1.
Then, by applying the quadratic formula, we have
[tex]x_{1,2}=\frac{-(-1)\pm\sqrt[]{(-1)^2-4(2)(-6)}}{2(2)}[/tex]
Then ,the first solution is
[tex]x_1=\frac{-(-1)+\sqrt[]{(-1)^2-4(2)(-6)}}{2(2)}[/tex]
and the
