Solution:
Given the equation:
[tex]4x^2-10x-36=0\text{ ---- equation 1}[/tex]To solve using the quadratic formula, we have the solution of the quadratic equation:
[tex]y=ax^2+bx+c\text{ ---- equation 2}[/tex]to be
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\text{ ----- equation 3}[/tex]Comparing equations 1 and 2, we have
[tex]\begin{gathered} a=4 \\ b=-10 \\ c=-36 \end{gathered}[/tex]By substituting these values into equation 3, we have
[tex]\begin{gathered} x=\frac{-(-10)\pm\sqrt{(-10)^2-4(4\times-36)}}{2(4)} \\ =\frac{10\pm\sqrt{676}}{8} \\ =\frac{10\pm26}{8} \\ \Rightarrow x=\frac{10+26}{8}=\frac{9}{2} \\ or \\ \Rightarrow x=\frac{10-26}{8}=-2 \end{gathered}[/tex]Hence, the solution, using the quadratic formula, is
[tex]x=\frac{9}{2}\text{ or x=-2}[/tex]