We need to solve the following equation:

We can start by adding 35 and substracting 8x at both sides of the equation:

So we have a quadratic function equalize to 0 which means that the solutions are the roots of the function. We can find them by using the quadratic solving equation:
![\begin{gathered} ax^2+bx+c=0 \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/uuterq6bz1kwr2mb9jy58c523r5v4v644y.png)
In this case, a=1, b=-8 and c=35. Then the solving equation looks like:
![\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}=\frac{-(-8)\pm\sqrt[]{(-8)^2-4\cdot35}}{2} \\ x=\frac{8\pm\sqrt[]{64-140}}{2}=\frac{8\pm\sqrt[]{-76}}{2} \\ x=\frac{8\pm\sqrt[]{-76}}{2}=(8)/(2)\pm i\sqrt[]{(76)/(4)} \\ x=4\pm i\sqrt[]{19} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/qurapqc84z8t9j5sbezm9ebupdcndkesr7.png)
Which means that the correct option is A.