We are given the following equation:

To solve for "x" we will use the quadratic formula, which is:
![x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}](https://img.qammunity.org/2023/formulas/mathematics/college/rxvf73usjbbwyik14knxdemoz21vfz2ufc.png)
Where the values of "a", "b" and "c" are the coefficients of the equation:

Therefore, in this case, we have:

Replacing in the quadratic formula:
![x=\frac{-(-4)\pm\sqrt[]{(-4)^2-4(1)(85)}}{2(1)}](https://img.qammunity.org/2023/formulas/mathematics/college/qtzcvqm8nzls279tzt51xx0g2rv0uv8urp.png)
Solving the operations inside the radical:
![x=\frac{-(-4)\pm\sqrt[]{-324}}{2}](https://img.qammunity.org/2023/formulas/mathematics/college/mi9bjkcflqa8s2h2eub6ctfdq78wzozn5e.png)
Now we divide the number inside the radical a the product of -1 and 324:
![x=\frac{-(-4)\pm\sqrt[]{(-1)(324)}}{2}](https://img.qammunity.org/2023/formulas/mathematics/college/8ln873z676apsg59vtd3p3f8pldw5exp3x.png)
Now we divide the square root:
![x=\frac{-(-4)\pm\sqrt[]{(-1)}\sqrt[]{324}}{2}](https://img.qammunity.org/2023/formulas/mathematics/college/vdhz70b0siaexoutv8ob73sgpmsd08m0v0.png)
The square root of -1 is the imaginary unit "i". Therefore, solving the square roots we get:

Now we separate the fraction:

Solving the operations:

Therefore, the solutions of the equation are:
