What is the method to solve an equation of type : ax^2+bx+c = 0 ?

This kind of equation is called a quadratic or a polynomial of degree 2.The goal when faced with a quadratic is to solve it as fast as possible. We do this in two steps.
First, we check if there is an easy way of factorising the expression. The factorised form will then give us the solution.Example 1: x^2 + 2x + 1 = 0 can be factorised as (x+1)^2 therefore the only solution to the equation is -1 Example 2: x^2 + 4x + 3 = 0 can be factorised as (x+3)(x+1) therefore the 2 only solutions to the equation are -3 and -1
If there is no easy or obvious way of factorising it is often faster to use the quadratic formula.First we need to find the discriminant. This will tell us if the equation has one, two or no solutions. For the equation ax^2 + bx + c = 0, the discriminant is delta = b^2 - 4ac. If delta > 0 the equation has 2 solution, if delta = 0 it has 1 and if delta < 0 it has none.If the equations has solutions we can then use the formula : x(1) = (-b-sqrt(delta))/2a x(2) = (-b+sqrt(delta))/2aYou will notice that if delta = 0 then x(1) = x(2).Example : x^2 + 4x + 3 = 0 so delta = 16 - 4*3 = 4 x(1) = (-4-sqrt(4))/2 = -3 x(2) = (-4+sqrt(4))/2 = -1