3x^2 - 2x = 27

3x² - 2x  =  27

Get all the terms to one side; subtract 27 from both sides:

3x² - 2x - 27  =  0

Factor, if posible. If not, use the quadratic formula:

x = [ -b ± √( b² - 4ac) ] / (2a)       a = 3     b = -2     c = -27

x = [ -(-2) ± √( (-2)² - 4(3)(-27)) ] / (2(3))   

x =  [ 2 ± √( 328 ) ] / 6  =  [ 2 ± 2√( 82 ) ] / 6  =  [ 1 ± √( 82 ) ] / 3