You may want to review the old way of solving them and complex numbers first.
One way to solve quadratic equations is by taking the square root of both sides. You need to be careful, though! For example, consider the equation x2 = −6. Since you now know about imaginary numbers, you take the square root of both sides, getting x = √6*i, which is almost right. Why almost? Well, remember that there are two numbers you can square to get 4 — 2 and −2. Similarly, here, there are two numbers you can square to get −6 — √6*i and −√6*i — so these are both solutions. Generally, a quadratic equation will have two solutions. (The only exception is if the thing on the right-hand side is just 0, since that only has one square root.)
In general, you might have to do some work at the beginning to get the square by itself, or at the end after you've taken the square root of both sides to get x by itself. For example, if you have (x − 3)2 + 1 = −5, you first subtract 1 from both sides (getting (x − 3)2 = −6), then take the square root of both sides (getting x − 3 = √6*i or −√6*i), then finally add 3 to both sides (getting x = 3 + √6*i or 3 − √6*i).