Answer:
x = 7
Explanation:
I like a graphing calculator for solving these, as it avoids problems with extraneous roots. It shows the left side of the equation is equal to the right side when x=7.
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In general, you solve these by isolating and squaring radical terms until there aren't any. Then solve the remaining polynomial. If you're lucky, it is of a degree that lends itself to a solution. Squaring both sides of the equation gives ...
4(x +2) -4√((x+2)(x-3)) +(x -3) = x +9
Subtracting the non-radical terms on the left and squaring again, we have ...
-4√((x +2)(x -3)) = -4(x -1) . . . . . . subtract 5x+5, factor the right
16(x +2)(x -3) = 16(x -1)^2
x^2 -x -6 = x^2 -2x +1 . . . . . divide by 16, eliminate parentheses
x = 7 . . . . . . . . . . . . . . . . . . . add 2x+6-x^2