Solve by using the quadratic formula. 

                   3x² = 11x + 4

Get 0 on the right by adding -6x + 4 to both sides


         3x² - 11x - 4 = 0

Use the quadratic formula:
                  ______ 
            -b ± Öb²-4ac
        x = —————————————
                2a 

where a = 3; b = -11; c = -4

                       _______________ 
             -(-11) ± Ö(-11)²-4(3)(-4)
        x = ———————————————————————————
                      2(3) 
                   ______ 
             11 ± Ö121+48
        x = ——————————————
                  6

                   ___ 
             11 ± Ö169
        x = ———————————
                 6

                   
             11 ± 13
        x = —————————
                6 

                   
                              
Using the +,

             11 + 13     24
        x = ————————— = ———— = 4
                6         6

Using the -,

             11 - 13     -2       1
        x = ————————— = ———— = - ———
                6         6       3

So the solutions are 4 and -1/3.

Edwin