There is also another method, which is simpler than the quadratic formula when a, b, and c (in ax^2+bx+c=0), are relatively easy and small, as in your problem. It is important to learn how to complete the square because the quadratic formula is derived from it.

2x^2-3x-8=0

First, make the coefficient of the x^2 term = 1 (divide by 2)

x^2-3/2x-4=0

Now here's the tricky part, recall how if you have (a+b)^2, it expands to a^2+2ab+b^2? Well, in this equation, x^2 is the a^2 term, and 3/2x is the 2ab term. We must 'create' the b^2 term, and to do this, we

**find half the coefficient of the x term squared**:

x^2 - 3/2x + 9/16 - 9/16 - 4 =0 (We must also subtract it so the equation's value remains the same)

Now, we can factorise x^2-3/2x+9/16:

(x - 3/4)^2 - 9/16 - 4 = 0

(x - 3/4)^2 = 73/16

And take the square root of both sides:

x - 3/4 = + sqrt{73}/4

or

x - 3/4 = -sqrt{73}/4

--------------------

x = (3 - sqrt{73})/4

or

x = (3 + sqrt{73}/4

This is a nice little animation showing how the quadratic formula is derived from completing the square:

Quadratic formula - derivation