SOLUTION: Find a quadratic equation that has the solution set (4/3, 2). And... A rectangular picture is 8 by 10 inches. The frame has the same width all the way around. The frame and the p

     x =         x = 2
    3x = 4         x = 2
3x - 4 = 0     x - 2 = 0
    (3x - 4)(x - 2) = 0
        3x2 - 10x + 8 = 0 

Please notice that this is simply the exact reverse of 
the step by step procedure for solving the resulting 
equation, which would be

        3x2 - 10x + 8 = 0 
    (3x - 4)(x - 2) = 0
3x - 4 = 0     x - 2 = 0
    3x = 4         x = 2
     x =         x = 2

here is the picture and frame:



Let the width of the frame be x
Draw in the 4 square corners, each of which has
side of length x, the width of the frame:



The total bottom width of the framed picture is gotten by adding
the green dimensions across the bottom 

x + 8 + x or 2x + 8

The total height of the framed picture is gotten by adding
the green dimensions along the right edge:

x + 10 + x or 2x + 10

Using the formula

Area = (bottom width) times (vertical height) we have the equation:

168 = (2x + 8)(2x + 10)

Do you know how to simplify and solve that equation?

If not post again asking how to solve it.  The

solutions you get are x = 2 and x = -11.

We ignore the negative solution and conclude that
the frame is 2 inches wide.

Edwin