Don't forget completing the square, which is often easier and faster than the quadratic formula.

 

Sorry.  Somehow this was posted to the wrong question.

 

3a² - 2a = 5 

1. Subtract 5 from both sides, so we have ZERO on the right side:

3a² - 2a - 5 = 0

2. Factor:

(3a - 5) (a + 1) = 0

Now we know that at least one of the values in the parentheses has to equal ZERO, because anything multiplied by Zero is going to equal Zero.

3. Solve each parentheses separately:

3a - 5 = 0  -->  3a = 5  -->  a = 5/3

a + 1 = 0  -->  a = -1

Answer: a = 5/3 or -1

**Remember you can always double check your answer by plugging it into the original equation!

You can solve this problem two different ways. Method 1: Factoring First move evething to one side. 3a^2 - 2a - 5 = 0 Then find factors of the first and last term (3 and 5) that add to be -2. So we have (3a-5)(a+1) = 0 Set 3a-5=0 and a+1=0 Then we see that a=5/3 or a=-1 Method 2: Quadratic Equation x = [-b(+/-)sqrt(b^2-4ac)]/2a Using this formula, we have a=3, b= -2, and c= -5 Plug in these values and you will obtain the same answer as in method 1. Remember there are two solutions.