Answer :
You have the following equation:
[tex]4y^2-16y-24=0[/tex]In order to solve the equation, use the quadratic formula:
[tex]y=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]In this case:
a = 4
b = -16
c = -24
Replace the previous values of the parameters into the quadratic formula and simplify:
[tex]\begin{gathered} y=\frac{-(-16)\pm\sqrt[]{(-16)^2-4(4)(-24)}}{2(4)} \\ y=\frac{16\pm\sqrt[]{640}}{8} \end{gathered}[/tex]Hence, the solutions for the given equation are:
[tex]\begin{gathered} y_1=2+\frac{\sqrt[]{640}}{8} \\ y_2=2-\frac{\sqrt[]{640}}{8} \end{gathered}[/tex]