State the quadratic formula and hence solve 

x(x + 3) = 6x + 2

Please show your working out, and thank you in 
advance for your help

Quadratic formula:

Given Ax² + Bx + C = 0, the solutions are
           ________ 
     -B ± ÖB² - 4AC
x = —————————————————
           2A

     x(x + 3) = 6x + 2

      x² + 3x = 6x + 2

Get 0 on right by subtracting 6x and 2 from both sides

  x² - 3x - 2 = 0 

Put 1 in front of x²

 1x² - 3x - 2 = 0

Compare that equation to

 Ax² + Bx + C = 0

We see that A = 1, B = -3, and C = -2

Substituting in 

           ________ 
     -B ± ÖB² - 4AC
x = —————————————————
           2A

              ________________ 
     -(-1) ± Ö(-1)² - 4(1)(-2)
x = ———————————————————————————
              2(1)

          _____ 
     1 ± Ö1 + 8
x = ————————————
          2

          _ 
     1 ± Ö9
x = ————————
       2

           
     1 ± 3
x = ————————
       2

± means + or -

First solution uses +:


     1 + 3     4
x = ——————— = ——— = 2
       2       2

Second solution uses -:


     1 - 3     -2
x = ——————— = ————— = -1
       2        2

Notice that your problem COULD have been solved
simply by factoring:

      x(x + 3) = 6x + 2

       x² + 3x = 6x + 2

   x² - 3x - 2 = 0

(x + 1)(x - 2) = 0

Using 0 factor principle:

x + 1 = 0, so x = -1

x - 2 = 0, so x = 2

However you were told to solve it by the
quadratic formula to get practice because
most quadratic equations can't be solved
by factoring.

Edwin
AnlytcPhil@aol.com