A quintic equation is an equation that has five parts. For example, it might look like this: x^5 + 7x^4 + 2x^2 + 4x + 3 = 0. To solve this equation, you need to figure out what number 'x' has to be so that the equation is true. To do this you need to use special methods that mathematicians have invented to help them solve equations like this. Sometimes you can solve it just by using regular math, but for most quintic equations, it's too complicated.