The quadratic formula is a way of solving quadratic equations of the form: ax²+bx+c=0. By plugging in the values a,b and c into it, the solutions for x can be obtained:

x = [-b +/- sqrt(b²-4ac)]/2a 

For example, solving 2x²+3x-5=0:

a = 2, b = 3, c = -5 so inputting these values into the formula above:

x = [-3 +/- sqrt(3²-4(2*-5)]/(2*2)

x = 1 or x = -5/2

These can be checked by inserting them into the original equation, or using a graphical method looking at the x-intercept coordinates.