Solve the equation `sqrt((x+3))-sqrt((x-2))=7`

Explanation

We have `3sqrt((x+3))-sqrt(x-2)=7`
`implies3sqrt((x+3))=7+sqrt((x-2))`
On squaring both sides of the equation, we obtain
`9x+27=49+x-2+14sqrt(x-2)`
`implies8x-20=14` sqrt((x-2))`
`(4x-10)=8sqrt(x-2)`
Again squaring both sides, we obtain
`16x^(2)+100-80x=49x-98`
`implies16x^(2)-129x+198=0`
`implies(x-6)(x-33/16)=0`
`x_(1)=6` and `x_(2)=33/16`
Hence `x_(1)=6` satisfies the original equatio, but `x_(2)=33/16`
does not satisfy the original equation.
`:.x_(2)=33/16` is the exraneous root.