x( x-3 ) = 48
multiply through x^2 - 3x = 48
complet the square ( one half the middle term and add the square of the result to both sides )
x^2 -3x + 9/4 = 48 + 9/4
factor ( x + 3/2 )^2 = (192 + 9)/4
take the square root ( x + 3/2 ) = (201)^1/2 / 2
subtract 3/2 x = ((201^1/2) - 3 / 2