A quadratic equation is a non-linear relationship between x and y.
For the secod part of your equation where you wonder is it meant to solve for 0, that's isn't always the case.
The reason sometimes a quadratic equation will be equal to 0, is when you are looking for the x-intercepts of your parabola. The reason why it's equal to 0 when you look for the x-intercepts is because the x-intercepts are always on the x-axis. Any point on the x-axis has a y-value of 0. This is why when we look for the x-interecepts, the y value is set to 0. We are solving for x when y = 0.
