Formulas to solve Polynomial Equations. 
The general form of the nth degree equation is: a_{0}x^{n} + a_{1}x^{n1} + a_{2}x^{n2} + ... + a_{n1}x + a_{n} = 0
The nth degree equations have always n roots. In particular cases, some or all of this n roots could be equal to one another.
If the coefficients a_{i} are real numbers, then the roots could be real or complex numbers. (Any combination, with the following restriction: if one of the roots is complex, then its conjugate is also a root. This implies that complex roots comes in pairs and that odd degree equations have at least one real root.)
First degree equations:  
ax + b = 0 One root: 

Second degree equations (or Quadratics):  
ax^{2} + bx + c = 0 

Third degree equations (or Cubics):  
ax^{3}
+ bx^{2} + cx
+ d
= 0
Three roots: 

Fourth degree equations (or Quartics):  
ax^{4}
+ bx^{3} + cx^{2}
+ dx + e
= 0
Four roots: 

Equations of degree higher than four:  
The roots of equations of degree higher than four can't, in general, be expressed using only the operations of addition, subtraction, multiplication, division and extraction of nth roots [Ruffini, Abel, Galois]. However, these roots can be found with numerical algorithms.  
