The area of a rectangle is 56 cm. the length is 2cm more than x and the width is 5 cm less than twice x. solve for x

Area of a rectangle is A = L*W.

Here, A = 56 cm^2 (not 56 cm).

              = (56 cm^2)=( L )( W )  = (x+2)*(2x-5) = 2x^2 - 5x + 4x - 10

Simplifying, 2x^2 - 5x + 4x - 10 = 56, or 2x^2 - x - 66 = 0.

Solve this using the quadratic formula:

        -(-1) plus or minus sqrt ( (-1)^2 - 4(2)(-66) )
x =
                                2(2)

Finish the work:  find x.  Most likely you will need to check both of the roots.  Keep in mind that x will likely be a positive number.